Turbulent flows generated/designed in multiscale/fractal ... - Ercoftac
Turbulent flows generated/designed in multiscale/fractal ... - Ercoftac
Turbulent flows generated/designed in multiscale/fractal ... - Ercoftac
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
1 ST UK-JAPAN BILATERAL WORKSHOP<br />
28-29 March 2011<br />
Department of Aeronautics | Imperial College London<br />
S. Laizet, Y. Sakai, J.C. Vassilicos<br />
<strong>Turbulent</strong> <strong>flows</strong><br />
<strong>generated</strong>/<strong>designed</strong> <strong>in</strong><br />
<strong>multiscale</strong>/<strong>fractal</strong> ways:<br />
fundamentals and<br />
applications<br />
FINAL PROGRAMME<br />
Nagoya University
1ST UK-JAPAN BILATERAL WORKSHOP<br />
1ST UK-JAPAN BILATERAL WORKSHOP<br />
Programme<br />
MONDAY 28 MARCH 2011<br />
8.30-9.00: Arrival and Registration (free entrance)<br />
9.00-9.15: Introduction by J.C. Vassilicos (Imperial College London, UK)<br />
First session: Fundamentals<br />
9.15-9.50: W.K. George (Imperial College London, UK) Free<strong>in</strong>g turbulence from the tyranny of the past<br />
9.50-10.25: M. Oberlack (TU Darmstadt, Germany) Beyond mean flow scal<strong>in</strong>g laws - how to obta<strong>in</strong> higher order moment<br />
scal<strong>in</strong>g from new statistical symmetries<br />
10.25-11.00: S. Goto (Okayama University, Japan) Multiscale self-similar coherent structures <strong>in</strong> developed turbulence<br />
11.00-11.30: COFFEE BREAK<br />
Second session: Different ways of generat<strong>in</strong>g turbulence<br />
11.30-12.05: N. Sekishita (Toyohashi University of Technology, Japan) Successful attempts of large scale-turbulence<br />
realization by a Makita-type turbulence gen- erator and a buoyancy jet <strong>in</strong> a cross w<strong>in</strong>d<br />
12.05-12.40: T. Ushijima (Nagoya Institute of Technology, Japan) Mean flow development of wake beh<strong>in</strong>d the Sierp<strong>in</strong>ski<br />
tetrahedron<br />
12.40-14.15: LUNCH<br />
14.15-14.50: K. Nagata (Nagoya University, Japan) Reexam<strong>in</strong>ation of <strong>fractal</strong>-<strong>generated</strong> turbulence us<strong>in</strong>g a smaller<br />
w<strong>in</strong>d tunnel<br />
14.50-15.25: P. Valente (Imperial College London, UK) Decay of homogeneous turbulence <strong>generated</strong> by a <strong>fractal</strong><br />
square grid: w<strong>in</strong>d tunnel experiments<br />
15.25-16.00: P. L<strong>in</strong>dstedt (Imperial College London, UK) Fractal <strong>generated</strong> turbulence <strong>in</strong> isothermal and react<strong>in</strong>g opposed<br />
jet <strong>flows</strong><br />
16.00-16.30: TEA BREAK<br />
Third session: Multi-po<strong>in</strong>ts statistics and <strong>in</strong>termittency<br />
16.30-17.05: J. Pe<strong>in</strong>ke (University of Oldenburg, Germany) A new class of turbulence - <strong>in</strong>sights from the perspective<br />
of n-po<strong>in</strong>t statistics<br />
17.05-17.40: C. Keylock (Sheffield University, UK) The wake structure, energy decay and <strong>in</strong>termittency beh<strong>in</strong>d a <strong>fractal</strong><br />
fence<br />
TUESDAY 29 MARCH 2011<br />
Fourth session: Flow design for applications<br />
9.15-9.50: Y. Sakai (Nagoya University, Japan) Mix<strong>in</strong>g of high-Schmidt number scalar <strong>in</strong> regular/<strong>fractal</strong> grid turbulence:<br />
Experiments by PIV and PLIF<br />
9.50-10.25: J. Nedic (Imperial College London, UK) Aero-acoustic performance of <strong>fractal</strong> spoilers<br />
10.25-11.00: COFFEE BREAK<br />
11.00-11.35: N. Soulopoulos (Imperial College London, UK) A turbulent premixed flame <strong>in</strong> <strong>fractal</strong>-grid <strong>generated</strong> turbulence<br />
11.35-12.10: T. Sponfeldner (Imperial College London, UK) A parametric study of the effect of <strong>fractal</strong>-grid <strong>generated</strong><br />
turbulence on the structure of premixed flames<br />
12.10-13.30: LUNCH<br />
Fifth session: Simulations<br />
13.30-14.05: B. Geurts (Twente University, Holland) Turbulence modulation through broad-band forc<strong>in</strong>g<br />
14.05-14.40: S. Laizet (Imperial College London, UK) Direct Numerical Simulation of <strong>multiscale</strong> <strong>generated</strong> turbulence<br />
14.40-15.00: TEA BREAK<br />
15.00-15.35: M. Pettit (Imperial College London, UK) LES/DNS of Opposed Jet Flows Employ<strong>in</strong>g Fractal Turbulence-<br />
Generat<strong>in</strong>g Plates<br />
15.35-16.10: H. Suzuki (Nagoya University, Japan) DNS on spatially develop<strong>in</strong>g <strong>fractal</strong> <strong>generated</strong> turbulence with heat<br />
transfer<br />
16.10-16.30: Discussion/Conclusion<br />
Introduction<br />
After more than a century of exhaustive research on the aerodynamics and hydrodynamics<br />
of geometrically simple shapes, whether streaml<strong>in</strong>ed as <strong>in</strong> w<strong>in</strong>gs or bluff as <strong>in</strong> spheres and<br />
cyl<strong>in</strong>ders, it is bl<strong>in</strong>d<strong>in</strong>gly natural to expect much of the future <strong>in</strong> fluid mechanics to lie <strong>in</strong> the<br />
aerodynamics and hydrodynamics of geometrically complex, and thereby <strong>multiscale</strong>, shapes.<br />
The simplest cases of <strong>multiscale</strong> shapes are <strong>fractal</strong> shapes, which is why they have been a good start.<br />
These are <strong>multiscale</strong> shapes with a complex appearance which can nevertheless be def<strong>in</strong>ed with only a<br />
small number of scal<strong>in</strong>g parameters.<br />
To my knowledge, the study of turbulent <strong>flows</strong> <strong>generated</strong>/<strong>designed</strong> <strong>in</strong> <strong>multiscale</strong>/<strong>fractal</strong> ways started<br />
<strong>in</strong> the UK with an experimental publication <strong>in</strong> 2001. These <strong>multiscale</strong>/<strong>fractal</strong> ways <strong>in</strong>clude <strong>multiscale</strong>/<br />
broadband forc<strong>in</strong>gs as well as <strong>multiscale</strong>/<strong>fractal</strong> boundary and/or <strong>in</strong>itial conditions. The first computational<br />
model of turbulence subjected to <strong>fractal</strong>/broadband forc<strong>in</strong>g which was neither motivated by nor limited to<br />
<strong>in</strong>tricacies of Renormalisation Group theory appeared <strong>in</strong> 2002, also from the UK.<br />
The idea was to <strong>in</strong>terfere with the <strong>multiscale</strong> dynamics, <strong>in</strong>ner geometry and topography of the turbulence<br />
itself and f<strong>in</strong>d out whether qualitatively different types of turbulence can be created. Whilst this idea is<br />
perhaps easy to accept for <strong>multiscale</strong>/broadband forc<strong>in</strong>gs it is less easy to accept for <strong>multiscale</strong>/<strong>fractal</strong><br />
<strong>in</strong>itial/boundary conditions.<br />
This is where the work of William K. George over the past quarter century fits <strong>in</strong> and gives mean<strong>in</strong>g<br />
to the endeavour, <strong>in</strong> particular his work on the importance and impr<strong>in</strong>t of <strong>in</strong>itial/boundary conditions<br />
on turbulent <strong>flows</strong>. If turbulent <strong>flows</strong> keep a degree of memory of the conditions which generate them,<br />
then the possibility exists of design<strong>in</strong>g bespoke turbulent <strong>flows</strong> taylor-made for particular applications.<br />
This is far better than turbulent flow control if it can be achieved. Multiscale/<strong>fractal</strong> generation/design<br />
is about us<strong>in</strong>g <strong>multiscale</strong>/<strong>fractal</strong> objects (such as grids, fences, profilers etc) to shape the nature of the<br />
result<strong>in</strong>g turbulent flow over a broad range of scales for a broad range of applications. Below is a list of<br />
applications touched upon <strong>in</strong> this 1st Japan-UK meet<strong>in</strong>g. More applications will be discussed <strong>in</strong> the 2nd<br />
Japan-UK meet<strong>in</strong>g one year from now.<br />
1. Fractal mixers: <strong>fractal</strong> grids can be used to design turbulent <strong>flows</strong> with low power losses and high<br />
turbulence <strong>in</strong>tensities for <strong>in</strong>tense yet economic mix<strong>in</strong>g over a region of <strong>designed</strong> length and location.<br />
2. Fractal combustors: the <strong>fractal</strong> design of a long region of high turbulence <strong>in</strong>tensity and its location are<br />
of great <strong>in</strong>terest for premixed combustion and may pave the way for future <strong>fractal</strong> combustors particularly<br />
adept at operat<strong>in</strong>g at the lean premixed combustion regime where NOx emissions are the lowest. In fact<br />
results recently obta<strong>in</strong>ed at Imperial’s Mechanical Eng<strong>in</strong>eer<strong>in</strong>g Department suggest that <strong>fractal</strong> design<br />
seems to generate turbulent flame speeds which <strong>in</strong>crease by even more than the <strong>in</strong>crease <strong>in</strong> turbulence<br />
<strong>in</strong>tensities!<br />
3. Fractal spoilers and airbrakes can have significantly reduced sound pressure levels without degrad<strong>in</strong>g<br />
the lift and drag characteristics of the w<strong>in</strong>g system.<br />
4. Fractal w<strong>in</strong>d breakers and <strong>fractal</strong> fences: a <strong>fractal</strong> fence, for example, can have <strong>in</strong>creased resistance<br />
because of all its empty areas, yet be an effective fence by modify<strong>in</strong>g the momentum profiles <strong>in</strong> its lee<br />
and thereby forc<strong>in</strong>g deposition of particulates, snow etc where desired.<br />
A lot of the driv<strong>in</strong>g force tak<strong>in</strong>g this new subject forward now comes from outside the UK and from<br />
Japan <strong>in</strong> particular. This very meet<strong>in</strong>g would not have happened without the success of our Japanese<br />
colleagues <strong>in</strong> Nagoya who developed an entire research programme on the topic, secured a very<br />
substantial Japanese research grant to support it and also obta<strong>in</strong>ed a travel grant to allow <strong>in</strong>teractions<br />
with us <strong>in</strong> Europe. This meet<strong>in</strong>g also shows that activity is grow<strong>in</strong>g <strong>in</strong> cont<strong>in</strong>ental Europe too, beyond the<br />
fog <strong>in</strong> the English channel. Indeed, beyond this fog, a substantial German research grant was given to<br />
Oldenburg last year for research on <strong>fractal</strong>-<strong>generated</strong> turbulence; and it is only because of the <strong>in</strong>itiative<br />
and help of Jean-Paul Bonnet and his colleagues <strong>in</strong> Poitiers that we were able to participate <strong>in</strong> the EU’s<br />
OPENAIR programme, without which we would not have been able to demonstrate the acoustic and<br />
aerodynamic performance of <strong>fractal</strong> spoilers.<br />
J.C. Vassilicos<br />
Department of Aeronautics, Imperial College London, UK<br />
2 <strong>Turbulent</strong> <strong>flows</strong> <strong>generated</strong>/<strong>designed</strong> <strong>in</strong> <strong>multiscale</strong>/<strong>fractal</strong> ways: fundamentals and applications<br />
<strong>Turbulent</strong> <strong>flows</strong> <strong>generated</strong>/<strong>designed</strong> <strong>in</strong> <strong>multiscale</strong>/<strong>fractal</strong> ways: fundamentals and applications 3
first session | Fundamentals<br />
Fundamentals | first sessioN<br />
monday 28 MARCH 2011 | 9.50-10.25<br />
MONDAY 28 MARCH 2011 | 9.15-9.50<br />
Free<strong>in</strong>g turbulence<br />
from the tyranny of<br />
the past<br />
W.K. George<br />
Department of Aeronautics, Imperial College London, UK<br />
There have been numerous studies over the past few decades about how<br />
scientists do research on difficult and <strong>in</strong>tractable problems, both how we function<br />
as <strong>in</strong>dividuals and collectively. While we would like to th<strong>in</strong>k that as <strong>in</strong>dividuals we<br />
are purely objective, all evidence suggests that we are not, and our judgements are<br />
strongly <strong>in</strong>fluenced by <strong>in</strong>tuition and past prejudices. In groups we tend to cluster<br />
around ‘group-th<strong>in</strong>k’, substitut<strong>in</strong>g consensus for critical analysis. Moreover there is<br />
a ‘herd’ <strong>in</strong>st<strong>in</strong>ct, mean<strong>in</strong>g there is a tendency to flock to a new idea, often without a<br />
good reason for do<strong>in</strong>g so.<br />
Of course none of this behaviour has ever happened <strong>in</strong> turbulence. Nonetheless,<br />
by exam<strong>in</strong><strong>in</strong>g the problems those <strong>in</strong> other fields have had, we can learn how to<br />
guard aga<strong>in</strong>st them <strong>in</strong> the future. Therefore the first part of this presentation will<br />
focus on the phenomena of how we function as turbulence researchers. And the<br />
second will try to identify potential problem areas where if we are not careful ideas<br />
we have long assumed to be true might be adopted as religious pr<strong>in</strong>ciples, even if<br />
they are false or only partially true.<br />
Also <strong>in</strong> this talk we will try to dist<strong>in</strong>guish between the mathematics of turbulence<br />
and the physics of turbulence. In mathematics, equations are precisely determ<strong>in</strong>ed,<br />
and the laws of mathematics which must be applied to f<strong>in</strong>d solutions are welldef<strong>in</strong>ed<br />
Physicists, on the other hand, build mathematical models of the universe<br />
as we f<strong>in</strong>d it. Once we have built the model and def<strong>in</strong>ed the boundary conditions,<br />
however, there is noth<strong>in</strong>g that is arbitrary: the laws of mathematics take over. The<br />
problem <strong>in</strong> turbulence (and other fields as well) is that often the consequences<br />
of the mathematics for our solutions are not consistent with what we observe <strong>in</strong><br />
nature. So is the problem with our model, or is it with the boundary conditions<br />
we have assumed to be true? S<strong>in</strong>ce often we have had to assume these to be<br />
applied at <strong>in</strong>f<strong>in</strong>ity, we cannot be sure. Nonetheless, there are usually some criteria<br />
for evaluation we can agree upon. For example if our model is the Navier-Stokes<br />
equations, it should not generally be our first assumption that they are wrong,<br />
especially for the constant density flow of a Newtonian fluid. Nor should we throw<br />
away so quickly a theory developed for an <strong>in</strong>f<strong>in</strong>ite doma<strong>in</strong> if our experiment is<br />
performed <strong>in</strong> a box. In fact it will probably be more productive to exam<strong>in</strong>e what<br />
the consequences are of the f<strong>in</strong>ite doma<strong>in</strong> or our attempts to realize the solution <strong>in</strong><br />
nature. Numerous examples will be used to illustrate these po<strong>in</strong>ts [1,2,3,4,5].<br />
Beyond mean flow scal<strong>in</strong>g<br />
laws - how to obta<strong>in</strong> higher<br />
order moment scal<strong>in</strong>g from<br />
new statistical symmetries<br />
1 st UK-JAPAN BILATERAL WORKSHOP, IC LONDON, UNITED KINGDOM, 28./29.3.2011<br />
BEYOND MEAN FLOW SCALING LAWS - HOW TO OBTAIN HIGHER ORDER MOMENT<br />
M. Oberlack 1,2,3 , A. Rosteck 1 UK-JAPAN 3 BILATERAL SCALING FROM WORKSHOP, NEW STATISTICAL IC LONDON, SYMMETRIES<br />
UNITED KINGDOM, 28./29.3.2011<br />
1 1<br />
Chair of Fluid st UK-JAPAN BILATERAL WORKSHOP, IC LONDON, UNITED KINGDOM, 28./29.3.2011<br />
Dynamics, BEYOND MEAN Technische FLOW SCALING Universität Darmstadt, GERMANY<br />
Mart<strong>in</strong> Oberlack LAWS 1,2,3 - HOW & Andreas TO OBTAIN Rosteck 1 HIGHER ORDER MOMENT<br />
2<br />
Center of BEYOND Smart MEAN Interfaces, 1 Chair FLOW of Fluid SCALING TU Dynamics SCALING<br />
Darmstadt, LAWS , Technische FROM - HOW NEW Universität Germany<br />
TO STATISTICAL OBTAIN Darmstadt, HIGHER SYMMETRIES<br />
64289 Darmstadt, ORDER MOMENT Germany,<br />
1 st UK-JAPAN<br />
3<br />
GS Computational Eng<strong>in</strong>eer<strong>in</strong>g, 2 BILATERAL WORKSHOP, IC LONDON, UNITED<br />
SCALING CenterFROM of Smart NEW Interfaces, STATISTICAL TU Darmstadt, SYMMETRIES<br />
KINGDOM, 28./29.3.2011<br />
64287 Darmstadt, Germany<br />
TU Darmstadt, Germany<br />
3 GS Computational<br />
Mart<strong>in</strong><br />
Eng<strong>in</strong>eer<strong>in</strong>g,<br />
Oberlack<br />
TU 1,2,3 Darmstadt,<br />
& Andreas<br />
64293<br />
Rosteck<br />
Darmstadt, 1<br />
BEYOND 1 MEAN FLOW SCALING LAWS - HOW TO OBTAIN HIGHER ORDER GermanyMOMENT<br />
Chair of Fluid Dynamics , Technische Universität Darmstadt, 64289 Darmstadt, Germany,<br />
We <strong>in</strong>vestigate the symmetry We <strong>in</strong>vestigate and the symmetry 2 Mart<strong>in</strong> SCALING Oberlack FROM<br />
<strong>in</strong>variance Center and of Smart <strong>in</strong>variance structure 1,2,3 NEW & Andreas STATISTICAL RosteckSYMMETRIES<br />
Interfaces, structure TUof Darmstadt, of the <strong>in</strong>f<strong>in</strong>ite 1<br />
1 64287 set of set Darmstadt, multi-po<strong>in</strong>t of multi-po<strong>in</strong>t Germany correlation correlation (MPC) equations<br />
for the fluctuations velocity 3 , Technische Universität Darmstadt, 64289 Darmstadt, Germany,<br />
2 GS and Computational pressure u(x, t) fluctuations and<br />
(MPC) equations for<br />
Chair of Fluid Dynamics<br />
the velocity and pressure<br />
Eng<strong>in</strong>eer<strong>in</strong>g,<br />
p(x, u(x, t) t) TUand Darmstadt, p(x, t) 64293 Darmstadt, Germany<br />
Center of Smart Interfaces, Mart<strong>in</strong> TUOberlack Darmstadt, 1,2,3 & 64287 Andreas Darmstadt, Rosteck 1 Germany<br />
3 GS 1 Computational Chair of Fluid Dynamics Eng<strong>in</strong>eer<strong>in</strong>g,<br />
, Technische TU Darmstadt, Universität64293 Darmstadt, Darmstadt, 64289 Darmstadt, Germany Germany,<br />
We <strong>in</strong>vestigate the<br />
S i{n+1} = ∂R symmetry and<br />
i {n+1}<br />
n <strong>in</strong>variance structure<br />
+ Ū k(l) (x<br />
∂t<br />
(l) ) ∂R of the <strong>in</strong>f<strong>in</strong>ite<br />
i {n+1}<br />
− ν ∂2 R i{n+1}<br />
set of multi-po<strong>in</strong>t correlation (MPC) equations<br />
for the velocity 2 Center of Smart Interfaces, TU Darmstadt, 64287 Darmstadt, + R Germany<br />
3 and pressure fluctuations u(x,<br />
∂Ūi (l)<br />
∂x<br />
t) and p(x,<br />
k(l) ∂x<br />
t)<br />
k(l) ∂x<br />
i{n+1} [i (l) →k (l) ]<br />
GS Computational k(l) ∂x k(l)<br />
l=1<br />
Eng<strong>in</strong>eer<strong>in</strong>g, TU Darmstadt, 64293 Darmstadt, Germany<br />
We <strong>in</strong>vestigate the symmetry and <strong>in</strong>variance structure<br />
∂u i(l) u k(l) (x (l) )<br />
− R i{n} [i (l) →0]<br />
+ ∂P i {n} [l]<br />
+ ∂R (1)<br />
i {n+2} [i (n+1) →k (l) ][x (n+1) → x (l) ]<br />
S i{n+1} = ∂R of the <strong>in</strong>f<strong>in</strong>ite set of multi-po<strong>in</strong>t correlation (MPC) equations<br />
for the + Ū k(l) (x ,<br />
i {n+1}<br />
n<br />
∂t<br />
(l) ) ∂R i {n+1}<br />
− ν ∂2 R i{n+1}<br />
∂Ūi (l)<br />
We<br />
velocity<br />
<strong>in</strong>vestigate<br />
and pressure<br />
the symmetry<br />
fluctuations<br />
and <strong>in</strong>variance<br />
u(x, t)<br />
structure<br />
and p(x,<br />
of<br />
t)<br />
the <strong>in</strong>f<strong>in</strong>ite set of multi-po<strong>in</strong>t + R<br />
∂x k(l)<br />
∂x ∂x k(l) i(l)<br />
∂x k(l) ∂x<br />
i{n+1} correlation [i<br />
∂x<br />
(l) →k (l) ] (MPC) equations<br />
for the velocity and pressurel=1<br />
fluctuations u(x, t) and p(x, t)<br />
k(l) k(l)<br />
∂x k(l)<br />
∂u i(l) u k(l) (x (l) )<br />
where n =1...∞. − RIn i{n} (1)[i the (l) →0] MPC tensor is def<strong>in</strong>ed + ∂P i {n} [l]<br />
as R i{n+1} + ∂R (1)<br />
S i {n+2} [i (n+1) →k (l) ][x (n+1) → x (l) ]<br />
= u i(0) (x (0) ) · ...· u i(n) (x (n) ) , and with , the<br />
four variations S i{n+1} of = ∂R <br />
i{n+1} = ∂R <br />
i {n+1}<br />
n<br />
+ Ū k(l) (x<br />
∂t i {n+1}<br />
n (l) ) ∂R i {n+1}<br />
it we have + a complete Ū k(l)<br />
∂x<br />
statistical k(l) (x ∂x<br />
description i(l) ∂x<br />
of turbulence. k(l)<br />
∂t<br />
(l) ) ∂R − ν ∂2 R i{n+1}<br />
∂Ūi (l)<br />
+ R<br />
∂x i {n+1}<br />
− ν ∂2 k(l) ∂x k(l) ∂x R i{n+1} [i i{n+1}<br />
(l) →k (l) ]<br />
k(l) ∂x<br />
+ R k(l)<br />
∂Ūi (l)<br />
l=1<br />
∂x k(l) ∂x k(l) ∂x<br />
i{n+1} [i (l) →k (l) ]<br />
k(l) ∂x k(l)<br />
Equation (1) admits∂u l=1<br />
all i(l) symmetries u k(l) (x (l) of ) the Navier-Stokes equations where they orig<strong>in</strong>ally emerged from at the<br />
where n =1...∞. In (1) the<br />
first place. Nevertheless equation ∂uMPC i(l) (1) upossesses k(l)<br />
tensor (x (l) ) is def<strong>in</strong>ed as R<br />
additional symmetries i{n+1} = u<br />
(see i(0) (x<br />
Oberlack, (0) ) · ...· u<br />
Rosteck i(n) (x<br />
2010 (n) ) , and with the<br />
& Rosteck<br />
four variations− of Rit Oberlack 2011)<br />
i{n} we[i (l) have →0] a complete statistical + ∂P i {n} [l]<br />
description + ∂R (1)<br />
− R i{n} [i (l) →0]<br />
+ ∂P i {n} [l]<br />
+ ∂R (1)<br />
i {n+2} [i (n+1) →k (l) ][x (n+1) → x (l) ]<br />
i {n+2} [i (n+1) →k (l) ][x (n+1) → x (l) ],<br />
∂x k(l) ∂x i(l) of turbulence. ∂x k(l)<br />
,<br />
∂x k(l) ∂x i(l) ∂x k(l)<br />
Equation (1) admits all symmetries of the Navier-Stokes equations<br />
G sh : ˜x = x, ˜r i(l) = r i(l) , ˜Ū i = e asŪ i, ˜R ij (x, y) =e where they orig<strong>in</strong>ally emerged as (1 − e as )Ūi(x)Ūj(y) − R ij (x, y) from at the<br />
where n =1...∞. first place. In (1) Nevertheless MPC equation tensor is(1) def<strong>in</strong>ed possesses as Radditional symmetries (see Oberlack, Rosteck 2010 , ··· & Rosteck<br />
where n =1...∞. In (1) the MPC tensor is def<strong>in</strong>ed i{n+1} = u<br />
as R i(0) (x<br />
i{n+1} = u (0) ) · ...· u<br />
i(0) (x<br />
Oberlack 2011)<br />
(0) ) · ...· i(n) (x<br />
u (n) ) , and with the<br />
i(n) (x (n) ) , and with the<br />
four variations<br />
four<br />
of<br />
variations<br />
it we have<br />
G L(a) : ˜x of= it<br />
a complete<br />
x, we˜r have<br />
i(l) = arcomplete statistical<br />
i(l) , ˜Ū i = statistical<br />
description Ūi + L (i) , description<br />
of turbulence.<br />
of turbulence.<br />
Equation (1) Equation admits all (2)<br />
G<br />
(1) symmetries admits<br />
sh : ˜R ij<br />
˜x (x, =<br />
all<br />
x,<br />
symmetries of the Navier-Stokes<br />
y) ˜r =R i(l) = ij (x, r i(l) y) ,<br />
of<br />
− ˜Ū the i L =<br />
Navier-Stokes<br />
e (i) Ū asŪ equations<br />
j (y) i, − ˜R ij L (x, (j) Ūy) equations where<br />
i (x) =e − as L (1<br />
where they orig<strong>in</strong>ally<br />
(i) L − e (j) , as they<br />
··· )Ūi(x)Ūj(y)<br />
orig<strong>in</strong>ally emerged<br />
−<br />
emerged from<br />
R ij (x, y)<br />
from at<br />
, ···<br />
at the the<br />
first place. Nevertheless first place. Nevertheless equation (1) equation possesses (1)<br />
G L(ab)<br />
G : ˜x = x, ˜r i(l) = r i(l) , ˜Ū L(a) : ˜x = x, ˜r i = Ūi, ˜R i(l) = r i(l) , ˜Ū<br />
possesses additional additional symmetries symmetries (see Oberlack, (see Oberlack, Rosteck Rosteck 2010 2010 & & Rosteck<br />
Oberlack 2011) Oberlack 2011)<br />
i = + ij<br />
L (x, (i) , y) =R ij (x, y)+L (ij) , ···<br />
(2)<br />
˜R ij (x, y) =R ij (x, y) − L (i) Ū j (y) − L (j) Ū i (x) − L (i) L (j) , ···<br />
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 scal<strong>in</strong>g<br />
group G(SSG) L(ab) and : ˜x G= L(a)<br />
x, ˜r , i(l) G L(ab)<br />
= r i(l) as, statistical ˜Ū<br />
= e asŪ i, ˜R<br />
i = Ūi, translation ˜R<br />
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) , ··· , ···<br />
ij (x, y) =R groups ij (x, (STG). y)+L (ij) , ···<br />
G G<br />
Assum<strong>in</strong>g L(a) : ˜x x, ˜r i(l) r i(l) , ˜Ū i =<br />
a plane parallel turbulent shear Ūi + L<br />
flow, (i) ,<br />
L(a) : ˜x = x, ˜r i(l) = r i(l) , ˜Ū i = the <strong>in</strong>f<strong>in</strong>ite set of equations (1) and the correspond<strong>in</strong>g symmetries<br />
provide the<br />
The latter are purely statistical Ūi + L (i) ,<br />
properties of the equations (1), while G ˜R ij <strong>in</strong>variant (x, y) =Rsurface ij (x, y) condition − L sh can be identified as a statistical scal<strong>in</strong>g<br />
(i) Ū j (y) − L (j) Ū i (x) − L (i) L (j) , ···<br />
(2)<br />
(2)<br />
˜R group ij (x,(SSG) y) =Rand ij (x, G L(a)<br />
y) , −G L L(ab) (i) Ūas statistical translation groups (STG).<br />
Assum<strong>in</strong>g<br />
G L(ab) :<br />
a<br />
˜x<br />
plane x,<br />
parallel<br />
˜r i(l) = r<br />
dx 2 turbulent i(l) , ˜Ū<br />
j (y) − L (j) Ū i (x) − L (i) L (j) , ···<br />
i<br />
= dr =<br />
shear Ūi,<br />
(k) flow, ˜R ij (x,<br />
the<br />
y)<br />
<strong>in</strong>f<strong>in</strong>ite<br />
=R ij (x,<br />
dŪ1 set<br />
y)+L<br />
of equations<br />
=<br />
= dR (ij) , ···<br />
G (11)(x, (1) y) and the correspond<strong>in</strong>g symmetries<br />
provide the <strong>in</strong>variant<br />
L(ab) : ˜x = x, ˜r i(l) = r i(l) , ˜Ū i = = ··· (3)<br />
k 1 x 2<br />
surface Ūi, ˜R ij (x, y) =R ij (x, y)+L (ij) , ···<br />
+ k x kcondition<br />
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)<br />
identified as a statistical scal<strong>in</strong>g<br />
The latter aregroup purely (SSG) statistical and G<br />
with the group parameters L(a)<br />
properties , G<br />
k L(ab)<br />
of<br />
dx asthe statistical equations<br />
1 , k 2 2 , k<br />
= x , k dr translation (1), while groups G sh (STG). can be<br />
a ,(k)<br />
l 1 and<br />
=<br />
l 11 descend<strong>in</strong>g dŪ1 from the<br />
= dR identified<br />
groups (11)(x,<br />
(2) y) as a statistical scal<strong>in</strong>g<br />
and<br />
= ···<br />
the classical symmetry<br />
group (SSG) Assum<strong>in</strong>g and G (3)<br />
groups here L(a) a , plane G<br />
written L(ab) parallel as statistical<br />
<strong>in</strong> <strong>in</strong>f<strong>in</strong>itesimal k turbulent 1 x 2 + k shear translation<br />
x forms. k 1 r flow,<br />
(k) (k<br />
the groups<br />
1 −<br />
<strong>in</strong>f<strong>in</strong>ite(STG).<br />
k 2 + k<br />
set of a )Ū1 +<br />
equations<br />
l 1 I(x, (1) and y) the correspond<strong>in</strong>g symmetries<br />
provide parallel theturbulent <strong>in</strong>variant surface shear flow, condition the <strong>in</strong>f<strong>in</strong>ite set of equations (1) and the correspond<strong>in</strong>g symme-<br />
Assum<strong>in</strong>g a plane<br />
tries provide the with <strong>in</strong>variant the group surface parameters condition k 1 , k 2 , k x , k a , l 1 and l 11 descend<strong>in</strong>g The abbreviation from the groups I(x, y) (2) isandef<strong>in</strong>ed the classical I(x, symmetry y) =<br />
groups here written <strong>in</strong> <strong>in</strong>f<strong>in</strong>itesimal dx 2<br />
= dr forms. (k)<br />
dŪ1<br />
=<br />
[2k 1 − 2k= 2 + dR k a<br />
(11)(x, y)<br />
]R (11) (x, = y)+l ··· 11 − k a Ū i (x)Ūj(y) (3) −<br />
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)<br />
2<br />
the <strong>in</strong>dices <strong>in</strong> brackets denote<br />
= dr (k)<br />
dŪ1<br />
=<br />
no<br />
The = dR (11)(x, y)<br />
summation<br />
abbreviation<br />
but <strong>in</strong>stead = I(x, ··· y)<br />
each<br />
is def<strong>in</strong>ed<br />
component<br />
as I(x,<br />
is (3) to<br />
y)<br />
be<br />
=<br />
with the group k 1 xparameters 2 + k x k 11 r , (k) k 2 , k x<br />
(k , k 1a −, l 1<br />
k 2 and + lk 11 a )Ū1 descend<strong>in</strong>g + l 1<br />
taken<br />
[2k 1<br />
from<br />
separately.<br />
−<br />
I(x,<br />
2kthe 2 +<br />
y) groups k a ]R (11)<br />
(2)(x, and y)+l the classical 11 − k a Ū i<br />
symmetry (x)Ūj(y) −<br />
groups here written <strong>in</strong> <strong>in</strong>f<strong>in</strong>itesimal forms.<br />
From<br />
l 1 (Ūi(x)+Ūj(y))<br />
(3) we may derive<br />
and<br />
various<br />
the <strong>in</strong>dices<br />
new<br />
<strong>in</strong><br />
scal<strong>in</strong>g<br />
brackets<br />
laws<br />
denote<br />
with the group parameters k 1 , k 2 , k x , k a , l 1 and l 11 descend<strong>in</strong>g from the groups (2) and the classical symmetryfor<br />
the<br />
no<br />
MPC<br />
summation<br />
tensor. Presently,<br />
but <strong>in</strong>stead<br />
we<br />
each<br />
<strong>in</strong>voke<br />
component<br />
symmetries<br />
is to<br />
<strong>in</strong><br />
be<br />
groups here written <strong>in</strong> <strong>in</strong>f<strong>in</strong>itesimal forms.<br />
The abbreviation I(x, y) is def<strong>in</strong>ed as I(x, y) =<br />
the<br />
taken<br />
range<br />
separately.<br />
[2k of the validity of the logarithmic law of the<br />
wall<br />
From 1 − 2k<br />
i.e.<br />
(3) 2 + k<br />
k 1 −<br />
we a ]R<br />
k<br />
may (11) (x, y)+l<br />
2 + k<br />
derive<br />
a =0and<br />
various 11 − k<br />
compute<br />
new a Ū<br />
scal<strong>in</strong>g i (x)Ūj(y) −<br />
the Reynolds<br />
laws for<br />
The abbreviation l 1 (Ūi(x)+Ūj(y)) I(x, y) andisthedef<strong>in</strong>ed <strong>in</strong>dices <strong>in</strong> asbrackets I(x, y) denote =<br />
stresses<br />
the MPC<br />
<strong>in</strong><br />
tensor.<br />
the range<br />
Presently,<br />
or the logarithmic<br />
we <strong>in</strong>voke symmetries<br />
law of the<br />
<strong>in</strong><br />
[2k 1 −no 2ksummation - but -<strong>in</strong>stead each- component - is to be<br />
wall.<br />
the 2 + range k a ]R<br />
The parameters<br />
of (11) the(x, validity y)+l<br />
of the<br />
of 11<br />
new<br />
the − k<br />
equations<br />
logarithmic a Ū i (x)Ūj(y)<br />
describ<strong>in</strong>g<br />
law−of the<br />
l 1 (Ūi(x)+Ūj(y)) taken separately.<br />
the<br />
wall<br />
Reynolds<br />
i.e. k 1 −and stresses<br />
k 2<br />
the + k<strong>in</strong>dices have a =0and <strong>in</strong><br />
been determ<strong>in</strong>ed<br />
compute bracketsthe denote<br />
from<br />
Reynolds<br />
From (3) we may derive various new scal<strong>in</strong>g laws for the<br />
no summation<br />
DNS-data<br />
stressesbut <strong>in</strong><br />
of<br />
the <strong>in</strong>stead<br />
a boundary<br />
rangeeach or<br />
layer<br />
the component logarithmicis flow at Re<br />
law to be<br />
Θ = 2003<br />
of the<br />
separately. the MPC tensor. Presently, we <strong>in</strong>voke symmetries <strong>in</strong><br />
Figure 1. Comparison of the DNS data (dotted l<strong>in</strong>es) with taken separately.<br />
by<br />
wall.<br />
Hoyas<br />
The<br />
and<br />
parameters<br />
Jimenez<br />
of<br />
(2006).<br />
the new<br />
In<br />
equations<br />
figure 1<br />
describ<strong>in</strong>g<br />
the range of the validity of the logarithmic lawone of the can<br />
the scal<strong>in</strong>g laws result<strong>in</strong>g from the new symmetries (solid From (3) see<br />
the we that<br />
Reynolds may thisderive provides<br />
stresses various have<br />
excellent new beenscal<strong>in</strong>g determ<strong>in</strong>ed<br />
matchlaws <strong>in</strong> the<br />
from for log<br />
the<br />
wall i.e. k<br />
l<strong>in</strong>es)<br />
region.<br />
DNS-data 1 − k<br />
of 2 + k<br />
a boundary a =0and compute the Reynolds<br />
the MPC layer flow at Re Θ = 2003<br />
stresses tensor. <strong>in</strong> the Presently, range or wethe <strong>in</strong>voke logarithmic symmetries law of<strong>in</strong>the<br />
Figure 1. Comparison of the DNS data (dotted l<strong>in</strong>es) the with rangeby Hoyas and Jimenez (2006). In figure 1 one can<br />
wall. ofThe theparameters validity of of the thelogarithmic new equations lawdescrib<strong>in</strong>g<br />
of the<br />
the scal<strong>in</strong>g laws result<strong>in</strong>g from the new symmetries (solid see that this provides an excellent match <strong>in</strong> the log<br />
wall i.e. the k 1 Reynolds − k 2 + kstresses a =0and havecompute been determ<strong>in</strong>ed the Reynolds from the<br />
l<strong>in</strong>es)<br />
region.<br />
stressesDNS-data <strong>in</strong> the range of a boundary or the logarithmic layer flow at law Re Θ of = the 2003<br />
Figure 1. Comparison of the DNS data (dotted l<strong>in</strong>es) with wall. The by Hoyas parameters and Jimenez of the new (2006). equations In figure describ<strong>in</strong>g 1 one can<br />
the scal<strong>in</strong>g laws result<strong>in</strong>g from the new symmetries (solid the Reynolds see thatstresses this provides have been an excellent determ<strong>in</strong>ed matchfrom <strong>in</strong> the the log<br />
l<strong>in</strong>es)<br />
DNS-data region. of a boundary layer flow at Re Θ = 2003<br />
Figure 1. Comparison of the DNS data (dotted l<strong>in</strong>es) with by Hoyas and Jimenez (2006). In figure 1 one can<br />
the scal<strong>in</strong>g laws result<strong>in</strong>g from the new symmetries (solid see that this provides an excellent match <strong>in</strong> the log<br />
l<strong>in</strong>es)<br />
region.<br />
where n=1...∞. In (1) the MPC tensor is def<strong>in</strong>ed as<br />
have a complete statistical description of turbulence.<br />
and with the four variations of it we<br />
Equation (1) admits all symmetries of the Navier-Stokes equations where they orig<strong>in</strong>ally emerged from <strong>in</strong> the first place.<br />
Nevertheless equation (1) possesses additional symmetries (see [6,7])<br />
The latter are purely statistical properties of the equations (1), while G sh<br />
can be identified as a statistical scal<strong>in</strong>g group<br />
(SSG) and G L(a)<br />
, G L(ab)<br />
as statistical translation groups (STG).<br />
Assum<strong>in</strong>g a plane parallel turbulent shear flow, the <strong>in</strong>f<strong>in</strong>ite set of equations (1) and the correspond<strong>in</strong>g symmetries provide<br />
the <strong>in</strong>variant surface condition<br />
with the group parameters k 1<br />
, k 2<br />
, k x<br />
, k a<br />
, l 1<br />
and l 11<br />
descend<strong>in</strong>g from the groups (2) and the classical symmetry groups here<br />
written <strong>in</strong> <strong>in</strong>f<strong>in</strong>itesimal forms.<br />
The abbreviation I(x, y) is def<strong>in</strong>ed as: I(x, y) = [2k 1<br />
- 2k 2<br />
+ k a<br />
]R (11)<br />
(x,y) + l 11<br />
- k a<br />
U i<br />
(x)U j<br />
(y) - l 1<br />
(U i<br />
(x) + U j<br />
(y)) and the <strong>in</strong>dices <strong>in</strong> brackets<br />
denote no summation but <strong>in</strong>stead each component is to be taken<br />
From (3) we may derive various new scal<strong>in</strong>g laws for the MPC<br />
tensor. Presently, we <strong>in</strong>voke symmetries <strong>in</strong> the range of the validity<br />
of the logarithmic law of the wall i.e. k 1<br />
− k 2<br />
+ k a<br />
= 0 and compute<br />
the Reynolds stresses <strong>in</strong> the range or the logarithmic law<br />
of the wall. The parameters of the new equations describ<strong>in</strong>g the<br />
Reynolds stresses have been determ<strong>in</strong>ed from the DNS-data of<br />
a boundary layer flow at Re τ<br />
= 2003 by Hoyas and Jimenez [8].<br />
In figure 1, one can see that this provides an excellent match <strong>in</strong><br />
the log region.<br />
4 turbulent <strong>flows</strong> <strong>generated</strong>/<strong>designed</strong> <strong>in</strong> <strong>multiscale</strong>/<strong>fractal</strong> ways: fundamentals and applications<br />
turbulent <strong>flows</strong> <strong>generated</strong>/<strong>designed</strong> <strong>in</strong> <strong>multiscale</strong>/<strong>fractal</strong> ways: fundamentals and applications 5
first session | Fundamentals<br />
Multi-scale Self-similar Coherent Structures <strong>in</strong> Developed Turbulence<br />
Susumu Goto<br />
Department of Mechanical Eng<strong>in</strong>eer<strong>in</strong>g, Okayama University, Okayama, 700-8530, Japan<br />
E-mail: goto@mech.okayama-u.ac.jp<br />
In order to reveal the coherent structures <strong>in</strong> fully developed turbulence and to understand their<br />
roles <strong>in</strong> the dynamics and statistics of turbulence, direct numerical simulations (DNS) of homogeneous<br />
isotropic turbulence <strong>in</strong> a periodic cube are conducted. By the DNS employ<strong>in</strong>g the Fourier spectral<br />
method with 2048 3 grid po<strong>in</strong>ts, turbulence at the Taylor-length based Reynolds number equal to 580<br />
is simulated.<br />
The multi-scale coherent structures are, then, visualised by the iso-surfaces of the coarse-gra<strong>in</strong>ed<br />
enstrophy, which is estimated by the low-pass filter<strong>in</strong>g of the Fourier components of the vorticity field.<br />
Results are shown <strong>in</strong> the figure below. It is clearly observed that thus visualised coherent vortical<br />
structures have ma<strong>in</strong>ly tubular shapes with radii of the order of the coarse-gra<strong>in</strong><strong>in</strong>g scale, whereas<br />
MONDAY<br />
their28 length<br />
MARCH<br />
is as long<br />
2011<br />
as the <strong>in</strong>tegral<br />
| 10.25-11.00<br />
length.<br />
This multi-scale self-similar coherent structures play roles <strong>in</strong> the turbulence dynamics. For example,<br />
the <strong>fractal</strong> structure of preferentially concentrated heavy small particles <strong>in</strong> turbulence is well described<br />
<strong>in</strong> term of these multi-scale coherent structures.<br />
It is also important to describe, based on these coherent structures, one of the most important<br />
dynamics of turbulence, i.e. the energy cascade. To <strong>in</strong>vestigate this process <strong>in</strong> detail, we <strong>in</strong>troduce<br />
(Goto 2008, JFM) scale-dependent energy and its transfer. It is, then, numerically verified that the<br />
Multiscale self-similar<br />
coherent structures <strong>in</strong><br />
developed turbulence<br />
energy at a scale (l, say) is conf<strong>in</strong>ed <strong>in</strong> the coherent vortex tubes at l, whereas the energy at scale l<br />
transfers (probably to smaller scales) the regions surround<strong>in</strong>g the vortex tubes at l, where the stra<strong>in</strong><br />
rate at the scale l is high. This result implies that the energy cascade is caused by the creation of the<br />
th<strong>in</strong>ner vortex tubes by the vortex stretch<strong>in</strong>g <strong>in</strong> larger-scale stra<strong>in</strong> field around fatter vortex tubes.<br />
Indeed, we can easily f<strong>in</strong>d the <strong>in</strong>vents which support this scenario of the energy cascade.<br />
Two problems arise from this conclusion, however. First one is on the universality of turbulence<br />
statistics, s<strong>in</strong>ce the above mechanism of the energy cascade implies that coherent structures at the<br />
Taylor micro scale can be directly created by the large-scale structures at the <strong>in</strong>tegral length. Secondly,<br />
to my knowledge, the relation between the Kolmogorov energy spectrum and this mechanics<br />
S. Goto<br />
of turbulent energy cascade is still open; where is the spiral structure, for example?<br />
Department of Mechanical Eng<strong>in</strong>eer<strong>in</strong>g, Okayama University, JAPAN<br />
Different ways of generat<strong>in</strong>g turbulence | SECOND session<br />
MONDAY 28 MARCH 2011 | 11.30-12.05<br />
Successful attempts of large<br />
scale-turbulence realization<br />
by a Makita-Type turbulence<br />
generator and a buoyant jet<br />
Successful Attempts of Large Scale-Turbulence Realization<br />
<strong>in</strong> a cross by a Makita-Type w<strong>in</strong>d Turbulence Generator<br />
and a Bouyance Jet <strong>in</strong> a Cross W<strong>in</strong>d<br />
N. Sekishta and H. Makita<br />
Toyohashi University of Technology, JAPAN<br />
Nobumasa SEKISHITA 1 and Hideharu MAKITA 2<br />
1,2 Toyohashi University of Technology<br />
(a) (b) (c) (d)<br />
FIG 1: Iso-surfaces of the enstrophy of the coarse-gra<strong>in</strong>ed enstrophy at (a) coarse-gra<strong>in</strong>ed 680η, (b) 340η (c) 170η and at (d)(a) 84η; 680η, where η is(b) the 340η (c)<br />
170η and<br />
Kolmogorov<br />
(d) 84η;<br />
length<br />
where<br />
scale. All<br />
η<br />
ofis these<br />
the<br />
scales<br />
Kolmogorov<br />
are <strong>in</strong> the <strong>in</strong>ertial range.<br />
length<br />
The sidescale. of the shown<br />
All<br />
cube<br />
of<br />
is 5400η<br />
these scales<br />
<strong>in</strong> (a,b,c), and 1700η <strong>in</strong> (d).<br />
are <strong>in</strong> the <strong>in</strong>ertial range. The side of the shown cube is 5400η <strong>in</strong> (a,b,c), and<br />
1700η <strong>in</strong> (d).<br />
In order to reveal the coherent structures <strong>in</strong> fully developed turbulence and to<br />
understand their roles <strong>in</strong> the dynamics and statistics of turbulence, direct numerical<br />
simulations (DNS) of homogeneous isotropic turbulence <strong>in</strong> a periodic cube are<br />
conducted. By the DNS employ<strong>in</strong>g the Fourier spectral method with 2048 3 grid<br />
po<strong>in</strong>ts, turbulence at the Taylor-length based Reynolds number equal to 580 is<br />
simulated. The <strong>multiscale</strong> coherent structures are then visualised by the isosurfaces<br />
of the coarse-gra<strong>in</strong>ed enstrophy, which is estimated by the low-pass<br />
filter<strong>in</strong>g of the Fourier components of the vorticity field. Results are shown <strong>in</strong> the<br />
figure. It is clearly observed that thus visualised coherent vortical structures have<br />
ma<strong>in</strong>ly tubular shapes with radii of the order of the coarse-gra<strong>in</strong><strong>in</strong>g scale, whereas<br />
their length is as long as the <strong>in</strong>tegral length. This <strong>multiscale</strong> self-similar coherent<br />
structures play roles <strong>in</strong> the turbulence dynamics. For example, the <strong>fractal</strong> structure<br />
of preferentially concentrated heavy small particles <strong>in</strong> turbulence is well described<br />
<strong>in</strong> term of these <strong>multiscale</strong> coherent structures.<br />
It is also important to describe, based on these coherent structures, one of the<br />
most important dynamics of turbulence, i.e. the energy cascade. To <strong>in</strong>vestigate<br />
this process <strong>in</strong> detail, we <strong>in</strong>troduce [9] scale-dependent energy and its transfer.<br />
It is then numerically verified that the energy at a scale (l, say) is conf<strong>in</strong>ed <strong>in</strong> the<br />
coherent vortex tubes at l, whereas the energy at scale l transfers (probably to<br />
smaller scales) the regions surround<strong>in</strong>g the vortex tubes at l, where the stra<strong>in</strong> rate<br />
at the scale l is high. This result implies that the energy cascade is caused by the<br />
creation of the th<strong>in</strong>ner vortex tubes by the vortex stretch<strong>in</strong>g <strong>in</strong> larger-scale stra<strong>in</strong><br />
field around fatter vortex tubes. Indeed, we can easily f<strong>in</strong>d the <strong>in</strong>vents which support<br />
this scenario of the energy cascade.<br />
Two problems arise from this conclusion, however. First one is on the universality<br />
of turbulence statistics, s<strong>in</strong>ce the above mechanism of the energy cascade implies<br />
that coherent structures at the Taylor microscale can be directly created by the<br />
large-scale structures at the <strong>in</strong>tegral length. Secondly, to my knowledge, the relation<br />
between the Kolmogorov energy spectrum and this mechanics of turbulent energy<br />
cascade is still open; where is the spiral structure, for example?<br />
Hibarigaoka 1-1, Tenpaku, Toyohashi, Aichi 441-8580, Japan<br />
Atmospheric boundary layers were seki@me.tut.ac.jp simulated <strong>in</strong> a laboratory w<strong>in</strong>d tunnel by<br />
regulat<strong>in</strong>g parameters of a turbulent shear flow generator. The generator has a<br />
shear Atmospheric flow device boundary and layers an were active simulated grid <strong>in</strong> with a laboratory agitator w<strong>in</strong>d w<strong>in</strong>gs tunnel driven by regulat<strong>in</strong>g by 40 parameters stepp<strong>in</strong>g of a<br />
motors. The generator could control turbulence characteristics; mean velocity<br />
turbulent shear flow generator. The generator has a shear flow device and an active grid with agitator w<strong>in</strong>gs<br />
U=0~8m/s, turbulence <strong>in</strong>tensity u’/U ∞<br />
=1~13% and <strong>in</strong>tegral scale L ux<br />
=0.02~1.9m.<br />
driven by 40 stepp<strong>in</strong>g motors. The generator could control turbulence characteristics; mean velocity<br />
Reynolds stress distributions were also <strong>in</strong>tensified throughout the thick boundary<br />
U=0~8m/s, layer by the turbulence present <strong>in</strong>tensity setup. The u'/Umaximum =1~13% and turbulence <strong>in</strong>tegral scale Reynolds L ux =0.02~1.9m. number, Reynolds R λ<br />
, reached stress<br />
distributions about 650 were at Ualso ∞<br />
=8m/s <strong>in</strong>tensified and throughout the spectrum the thick had boundary a wide layer <strong>in</strong>ertial by the sub present range setup. comparable<br />
The maximum<br />
turbulence to those Reynolds <strong>in</strong> natural number, atmospheric R , reached boundary about 650 layers. at U =8m/s and the spectrum had a wide <strong>in</strong>ertial<br />
subrange Coherent comparable structures to those were <strong>in</strong> natural <strong>in</strong>vestigated atmospheric <strong>in</strong> boundary a round layers. jet of heated air with temperature<br />
difference, Coherent structures 0, 20, were 40 and <strong>in</strong>vestigated 60K. The <strong>in</strong> a round present jet of heated jet was air with vertically temperature ejected difference, <strong>in</strong> a 0, cross 20, 40<br />
flow field. Three k<strong>in</strong>ds of flow pattern <strong>in</strong> the jet with smoke were observed by flow<br />
and 60K. The present jet was vertically ejected <strong>in</strong> a cross flow field. Three k<strong>in</strong>ds of flow pattern <strong>in</strong> the jet<br />
visualization <strong>in</strong> the cross flow <strong>generated</strong> with or without a turbulence grid. In the<br />
with smoke were observed by flow visualization <strong>in</strong> the cross flow <strong>generated</strong> with without a turbulence<br />
case of mode I, hairp<strong>in</strong>-type vortices occurred <strong>in</strong> the jet. Two vortex tubes with and<br />
grid. without In the strong case of mutual mode I, hairp<strong>in</strong>-type <strong>in</strong>teraction vortices (bifurcation) occurred <strong>in</strong> were the jet. <strong>generated</strong> Two vortex for tubes mode with II and and without III,<br />
strong respectively. mutual <strong>in</strong>teraction Vortex (bifurcation) behaviour, were the <strong>generated</strong> convection for mode velocity II and III, of the respectively. coherent Vortex vortices, behavior, the<br />
convection Strouhal velocity number, of the etc., coherent was vortices, <strong>in</strong>vestigated the Strohal from number, the results etc., was of <strong>in</strong>vestigated motion pictures from the results taken of<br />
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<br />
structures structures decreased decreased with <strong>in</strong>creas<strong>in</strong>g with <strong>in</strong>creas<strong>in</strong>g the temperature the difference. temperature These vortex difference. shedd<strong>in</strong>g frequencies These vortex and the<br />
shedd<strong>in</strong>g frequencies and the Strouhal numbers decreased with <strong>in</strong>creas<strong>in</strong>g the<br />
Strohal numbers decreased with <strong>in</strong>creas<strong>in</strong>g the temperature difference.<br />
temperature difference.<br />
vortex formation region vortex region<br />
Y/D<br />
20<br />
10<br />
0<br />
flow<br />
0 20 40 60 80 100<br />
X/D<br />
Fig. 1. <strong>Turbulent</strong> Shear flow generator. Fig. 2 Vortex formation region and vortex region.<br />
6<br />
turbulent <strong>flows</strong> <strong>generated</strong>/<strong>designed</strong> <strong>in</strong> <strong>multiscale</strong>/<strong>fractal</strong> ways: fundamentals and applications<br />
turbulent <strong>flows</strong> <strong>generated</strong>/<strong>designed</strong> <strong>in</strong> <strong>multiscale</strong>/<strong>fractal</strong> ways: fundamentals and applications<br />
7
SECOND session | Different ways of generat<strong>in</strong>g turbulence<br />
Different ways of generat<strong>in</strong>g turbulence | SECOND session<br />
MONDAY 28 MARCH 2011 | 12.05-12.40<br />
Mean flow<br />
development of wake<br />
beh<strong>in</strong>d the Sierp<strong>in</strong>ski<br />
tetrahedron<br />
T. Ushijima<br />
Department of Eng<strong>in</strong>eer<strong>in</strong>g Physics, Electronics and Mechanics,<br />
Graduate School of Eng<strong>in</strong>eer<strong>in</strong>g, Nagoya Institute of Technology,<br />
JAPAN<br />
MONDAY 28 MARCH 2011 | 14.15-14.50<br />
Re-exam<strong>in</strong>ation of<br />
<strong>fractal</strong>-<strong>generated</strong><br />
turbulence us<strong>in</strong>g a<br />
smaller w<strong>in</strong>d tunnel<br />
K. Nagata, Y. Sakai, H. Suzuki and H. Suzuki<br />
Department of Mechanical Science and Eng<strong>in</strong>eer<strong>in</strong>g, Nagoya University,<br />
Furoh-cho, Chikusa-ku, Nagoya 464-8603 JAPAN<br />
This work is motivated by two physical facts: firstly <strong>fractal</strong> dimension of foliage<br />
distribution of crown tree is <strong>in</strong> the range between 2 and 2.4. Secondly, w<strong>in</strong>d drag<br />
exerted on the tree is proportional to w<strong>in</strong>d speed despite large Reynolds number<br />
based on the w<strong>in</strong>d speed and square root of the projected area of trees. The latter<br />
suggests that the crown tree structure is optimal to the w<strong>in</strong>d resistance and this<br />
feature can be relevant to the <strong>fractal</strong> geometry of the tree. Direct application can be<br />
artificial w<strong>in</strong>dbreakers dur<strong>in</strong>g the development of forestation.<br />
The Sierp<strong>in</strong>ski tetrahedron has the <strong>fractal</strong> dimension of 2, which is the same as<br />
that of foliage distribution, and can cover the projected area efficiently. We used this<br />
three dimensional <strong>fractal</strong> structure as a model of tree to understand the turbulence<br />
<strong>generated</strong> <strong>in</strong> the natural environment.<br />
In this prelim<strong>in</strong>ary report, the mean flow development of the wake beh<strong>in</strong>d the<br />
Sierp<strong>in</strong>ski tetrahedron was <strong>in</strong>vestigated. The Sierp<strong>in</strong>ski tetrahedron is <strong>in</strong>stalled at<br />
the upstream end of a small scale w<strong>in</strong>d tunnel, which has 130mm by 130mm cross<br />
section and 2000mm <strong>in</strong> length. Development of the mean and r.m.s. velocities <strong>in</strong><br />
the streamwise direction is measured at s<strong>in</strong>gle experimental condition (4.9 ms -1 at<br />
the bulk velocity) by both Pitot tube and hot wire anemometry.<br />
The mean velocity distribution <strong>in</strong> the cross section is quite <strong>in</strong>homogeneous. Near<br />
the Sierp<strong>in</strong>ski object, the local mean velocity varies by ±40 percent of the mean<br />
velocity over the cross section of the section and it rema<strong>in</strong>s strongly <strong>in</strong>homogeneous<br />
far downstream. Inhomogeneity is a source of turbulence energy and produces<br />
relatively large fluctuations. Turbulence <strong>in</strong>tensities decrease from 20 to 10 percent<br />
dur<strong>in</strong>g the test section. Turbulence energy obeys the l<strong>in</strong>ear decay law. Reynolds<br />
number based on Taylor micro scale is around 150.<br />
Our f<strong>in</strong>d<strong>in</strong>gs suggest that use of <strong>fractal</strong> objects can reduce the size of turbulent<br />
mixers, which is practical <strong>in</strong> the situation where a turbulent jet is not suitable for<br />
mix<strong>in</strong>g.<br />
We reexam<strong>in</strong>ed the <strong>multiscale</strong>/<strong>fractal</strong> <strong>generated</strong> turbulence by Hurst & Vassilicos<br />
[4], Seoud & Vassilicos [5] and Mazellier & Vassilicos [10] us<strong>in</strong>g a smaller w<strong>in</strong>d<br />
tunnel. The test section of the w<strong>in</strong>d tunnel is 0.3x0.3x4.0m 3 . The square-type<br />
<strong>fractal</strong> grid (blockage ratio σ = 0.25, thickness ratio t r<br />
= 13.0, <strong>fractal</strong> dimension<br />
D f<br />
= 2, L 0<br />
= 163.8 mm, L 1<br />
= 78.9 mm, L 2<br />
= 38.1 mm, L 3<br />
= 18.3 mm, t 0<br />
= 11.7 mm,<br />
t 1<br />
= 4.9 mm, t 2<br />
= 2.1 mm, t 3<br />
= 0.9 mm, where L i<br />
are the successive bar length<br />
and ti are the successive bar thickness: see [4] and [5] for detail) was <strong>in</strong>stalled at<br />
0.15m downstream of the entrance of the test section. The Reynolds numbers Re 0<br />
based on t 0<br />
and mean flow velocity upstream of the grid are 6,000 and 11,400. The<br />
<strong>in</strong>stantaneous streamwise velocities are measured us<strong>in</strong>g the hot-wire anemometry<br />
with a self-made I-probe. The diameter and length of the sensor are d = 5 μm and<br />
l = 1 mm, respectively. The results are compared with those by [10] who used the<br />
larger w<strong>in</strong>d tunnel. Figure 1 shows the normalised profiles of rms velocities. Here,<br />
x is the streamwise distance from the grid, x* is the wake-<strong>in</strong>teraction length scale<br />
(see [10]), x peak<br />
is the streamwise location where turbulence <strong>in</strong>tensities exhibit the<br />
peak value and subscript c denotes the value on the centre l<strong>in</strong>e. Our results us<strong>in</strong>g<br />
a smaller w<strong>in</strong>d tunnel agree well with that by [10]. Other statistics, for example<br />
skewness and flatness factors, also agree well with those of [10].<br />
Figure 1 Streamwise evolution of turbulence <strong>in</strong>tensities normalized by their<br />
values at x = x peak<br />
8 turbulent <strong>flows</strong> <strong>generated</strong>/<strong>designed</strong> <strong>in</strong> <strong>multiscale</strong>/<strong>fractal</strong> ways: fundamentals and applications<br />
turbulent <strong>flows</strong> <strong>generated</strong>/<strong>designed</strong> <strong>in</strong> <strong>multiscale</strong>/<strong>fractal</strong> ways: fundamentals and applications 9
SECOND session | Different ways of generat<strong>in</strong>g turbulence<br />
Different ways of generat<strong>in</strong>g turbulence | SECOND session<br />
monday 28 MARCH 2011 | 14.50-15.25 MONDAY 28 MARCH 2011 | 15.25-16.00<br />
The decay of<br />
homogeneous<br />
turbulence <strong>generated</strong><br />
by <strong>multiscale</strong> grids<br />
Fractal <strong>generated</strong><br />
turbulence <strong>in</strong><br />
isothermal and react<strong>in</strong>g<br />
opposed jet <strong>flows</strong><br />
P.C. Valente, J.C. Vassilicos<br />
Department of Aeronautics, Imperial College London, UK<br />
R.P. L<strong>in</strong>dstedt, P. Geipel and K.H.H. Goh<br />
Department of Mechanical Eng<strong>in</strong>eer<strong>in</strong>g, Imperial College London, UK<br />
A new experimental <strong>in</strong>vestigation of freely decay<strong>in</strong>g homogeneous, quasi-isotropic<br />
turbulence <strong>generated</strong> by a low-blockage space-fill<strong>in</strong>g <strong>fractal</strong> square grid is<br />
presented. We f<strong>in</strong>d good agreement with previous works by Seoud & Vassilicos [5]<br />
and Mazellier & Vassilicos [10] but also extend the length of the assessed decay<br />
region and consolidate the results by repeat<strong>in</strong>g the experiments with different<br />
anemometry systems and probes of <strong>in</strong>creased spatial resolution. It is confirmed<br />
that this moderately high Reynolds number Re λ<br />
turbulence does not follow the<br />
classical high Reynolds number scal<strong>in</strong>g of the dissipation rate ε ~ u′3/L which is<br />
<strong>in</strong> fact a direct reflection of the proportionality between the Taylor-based Reynolds<br />
number, Re λ<br />
, and the ratio of <strong>in</strong>tegral scale L and the Taylor micro-scale λ. Instead<br />
we observe a proportionality between, L, and, λ, dur<strong>in</strong>g decay. Alternative reasons<br />
for this non-classical behaviour are discussed, <strong>in</strong>clud<strong>in</strong>g various ways <strong>in</strong> which the<br />
turbulence may fall <strong>in</strong>to a self-preserv<strong>in</strong>g, s<strong>in</strong>gle-length-scale state <strong>in</strong>duced by the<br />
<strong>in</strong>itial conditions of this particular flow.<br />
It is shown that the measured 1D spectra can be reasonably collapsed us<strong>in</strong>g a<br />
s<strong>in</strong>gle length-scale over the entire decay region even though the Reynolds number<br />
is high enough for conventional decay<strong>in</strong>g turbulence to display 1D spectra with twoscale<br />
(<strong>in</strong>ner and outer) Kolmogorov scal<strong>in</strong>g. We propose a correction for the weak<br />
anisotropy of the flow by comput<strong>in</strong>g the 3D spectrum function from two component<br />
velocity signals lead<strong>in</strong>g to further improved s<strong>in</strong>gle-scale non-Kolmogorov collapse.<br />
Detailed checks on homogeneity and isotropy are also presented <strong>in</strong>dicat<strong>in</strong>g that<br />
the s<strong>in</strong>gle-length scale behaviour can not be an artifice of the hardly present<br />
<strong>in</strong>homogeneity.<br />
The opposed jet configuration presents a canonical geometry suitable for the<br />
evaluation of calculation methods seek<strong>in</strong>g to reproduce the impact of stra<strong>in</strong> and<br />
re-distribution on turbulent transport <strong>in</strong> react<strong>in</strong>g and non-react<strong>in</strong>g <strong>flows</strong>. The<br />
geometry has the advantage of good optical access and, <strong>in</strong> pr<strong>in</strong>ciple, an absence<br />
of complex boundary conditions. Disadvantages <strong>in</strong>clude low frequency flow motion<br />
at high nozzle separations and comparatively low turbulence levels caus<strong>in</strong>g bulk<br />
stra<strong>in</strong> to exceed the turbulent contribution at small nozzle separations. In the<br />
current work, <strong>fractal</strong> <strong>generated</strong> turbulence has been used to <strong>in</strong>crease the turbulent<br />
stra<strong>in</strong> and velocity measurements for isothermal and react<strong>in</strong>g <strong>flows</strong> are reported<br />
with an emphasis on the axis, stagnation plane and the distribution of mean and<br />
<strong>in</strong>stantaneous stra<strong>in</strong> rates. Energy spectra were also determ<strong>in</strong>ed and it showed<br />
that <strong>fractal</strong> grids <strong>in</strong>crease the turbulent Reynolds number range from 48–125 to<br />
109–220 for bulk velocities from 4 to 8 m/s as compared to conventional perforated<br />
plate turbulence generators. The applied <strong>in</strong>strumentation comprised hotwire<br />
anemometry, particle image velocimetry and a multi-step adaptive algorithm was<br />
developed and used to determ<strong>in</strong>e conditional statistics for react<strong>in</strong>g cases. Examples<br />
are given with respect to velocity and scalar statistics, the motion of the stagnation<br />
plane and with probability density functions for the <strong>in</strong>stantaneous <strong>in</strong>cl<strong>in</strong>ation of the<br />
flame sheet also determ<strong>in</strong>ed. F<strong>in</strong>ally, a proper orthogonal decomposition technique<br />
was adopted <strong>in</strong> order to exam<strong>in</strong>e the eigenmodes result<strong>in</strong>g from an analysis of the<br />
<strong>in</strong>stantaneous vector fields and the dom<strong>in</strong>ant structures identified. The work shows<br />
that the application of <strong>fractal</strong>-<strong>generated</strong> turbulence holds significant advantages <strong>in</strong><br />
the context of the opposed jet geometry.<br />
10 turbulent <strong>flows</strong> <strong>generated</strong>/<strong>designed</strong> <strong>in</strong> <strong>multiscale</strong>/<strong>fractal</strong> ways: fundamentals and applications<br />
turbulent <strong>flows</strong> <strong>generated</strong>/<strong>designed</strong> <strong>in</strong> <strong>multiscale</strong>/<strong>fractal</strong> ways: fundamentals and applications 11
THIRD session | Multi-po<strong>in</strong>t statistics and <strong>in</strong>termittency<br />
Multi-po<strong>in</strong>t statistics and <strong>in</strong>termittency | THIRD sessioN<br />
monday 28 MARCH 2011 | 16.30-17.05<br />
A new class of<br />
turbulence - <strong>in</strong>sights<br />
from the perspective of<br />
n-po<strong>in</strong>t statistics<br />
R. Stres<strong>in</strong>g, J. Pe<strong>in</strong>ke<br />
Institute of Physics, University of Oldenburg, GERMANY<br />
monday 28 MARCH 2011 | 17.05-17.40<br />
The wake structure,<br />
energy decay and<br />
<strong>in</strong>termittency beh<strong>in</strong>d a<br />
<strong>fractal</strong> fence<br />
C.J. Keylock<br />
Department of Civil Eng<strong>in</strong>eer<strong>in</strong>g, University of Sheffield, UK<br />
R.E. Seoud, J.C. Vassilicos<br />
Department of Aeronautics, Imperial College London, UK<br />
We apply a method based on the theory of Markov processes to <strong>fractal</strong>-<strong>generated</strong><br />
turbulence and obta<strong>in</strong> jo<strong>in</strong>t probabilities of velocity <strong>in</strong>crements at several scales.<br />
From experimental data we extract a Fokker-Planck equation which describes<br />
the <strong>in</strong>terscale dynamics of the turbulence. In stark contrast to all documented<br />
boundary-free turbulent <strong>flows</strong>, the <strong>multiscale</strong> statistics of velocity <strong>in</strong>crements, the<br />
coefficients of the Fokker-Planck equation, and dissipation-range <strong>in</strong>termittency are<br />
all <strong>in</strong>dependent of Reynolds number. These properties def<strong>in</strong>e a qualitatively new<br />
class of turbulence. Furthermore we use the <strong>multiscale</strong> statistics of homogeneous<br />
isotropic turbulence which can described by a stochastic “cascade” process of the<br />
velocity <strong>in</strong>crement from scale to scale by a Fokker-Planck equation. We show how<br />
this description can be extended to obta<strong>in</strong> the complete multi-po<strong>in</strong>t statistics of the<br />
velocity field, i.e. we achieve an explicit expression for the jo<strong>in</strong>t probability p(u(x 1<br />
),<br />
u(x 2<br />
), ..., u(x n<br />
)), where u(x i<br />
) is the velocity at the spatial po<strong>in</strong>t x i<br />
(spatial po<strong>in</strong>t are<br />
obta<strong>in</strong>ed along one l<strong>in</strong>e us<strong>in</strong>g Taylor’s hypothesis of frozen turbulence). We extend<br />
the stochastic cascade description by condition<strong>in</strong>g on the velocity value itself and<br />
f<strong>in</strong>d that the correspond<strong>in</strong>g process is also governed by a Fokker-Planck equation,<br />
which conta<strong>in</strong>s as a lead<strong>in</strong>g term a simple additional velocity-dependent coefficient<br />
<strong>in</strong> the drift function. Tak<strong>in</strong>g <strong>in</strong>to account the velocity dependence of the Fokker-<br />
Planck equation, the multi-po<strong>in</strong>t statistics <strong>in</strong> real space can be expressed by the<br />
two-scale statistics of velocity <strong>in</strong>crements, which are equivalent to the three-po<strong>in</strong>t<br />
statistics of the velocity field. Thus, we propose a stochastic three-po<strong>in</strong>t closure for<br />
the velocity field of homogeneous isotropic turbulence.<br />
This paper reports the results of experiments on the structure of the wake beh<strong>in</strong>d<br />
fences <strong>in</strong>serted <strong>in</strong> a boundary layer flow <strong>in</strong> a w<strong>in</strong>d tunnel, which was undertaken <strong>in</strong><br />
the Sh<strong>in</strong>jo w<strong>in</strong>d tunnel <strong>in</strong> Japan, with Kouichi Nishimura (University of Nagoya) and<br />
colleagues at the Nagaoka Institute for Snow and Ice Studies. The fences varied <strong>in</strong><br />
their porosity and the spac<strong>in</strong>g of struts but, <strong>in</strong> addition, two fences were deployed<br />
where the struts were organised <strong>in</strong> a <strong>fractal</strong> pattern. Hence, this study marks a<br />
departure from previous work that has focussed on the flow structure beh<strong>in</strong>d <strong>fractal</strong><br />
fences away from boundaries.<br />
In general our results <strong>in</strong>dicate that the nature of the fence, such as its porosity, has<br />
a larger control on wake structure than the Reynolds number of the flow (<strong>flows</strong> had<br />
mean <strong>in</strong>put velocities of either 6 ms -1 or 8 ms -1 ). However, we also f<strong>in</strong>d cases where<br />
the <strong>multiscale</strong> nature of the forc<strong>in</strong>g with the <strong>fractal</strong> fences results <strong>in</strong> differences <strong>in</strong><br />
wake structure that are greater than those due to porosity or Reynolds number. In<br />
particular, we show that the proportion of dissipation tak<strong>in</strong>g place over the range of<br />
forced scales is greater for the <strong>fractal</strong> fences and given the slope of the spectrum <strong>in</strong><br />
this region, the implication is that the scale-to-scale transfer over this region is not<br />
<strong>in</strong>ertial <strong>in</strong> a strict sense. This result parallels that from other studies on <strong>multiscale</strong><br />
forc<strong>in</strong>g <strong>in</strong> recent years by Vassilicos and coworkers.<br />
In order to study this effect <strong>in</strong> more detail, we also exam<strong>in</strong>e the properties of<br />
synthetic turbulence <strong>generated</strong> from the experimental time series and by a<br />
comparison to the forc<strong>in</strong>gs at <strong>in</strong>dividual scales, attempt to identify the manner <strong>in</strong><br />
which the unique properties of the <strong>fractal</strong>-forced <strong>flows</strong> become manifest.<br />
12 turbulent <strong>flows</strong> <strong>generated</strong>/<strong>designed</strong> <strong>in</strong> <strong>multiscale</strong>/<strong>fractal</strong> ways: fundamentals and applications<br />
turbulent <strong>flows</strong> <strong>generated</strong>/<strong>designed</strong> <strong>in</strong> <strong>multiscale</strong>/<strong>fractal</strong> ways: fundamentals and applications 13
FOURTH session | Flow design for applications<br />
Flow design for applications | FOURTH session<br />
TUESDAY 29 MARCH 2011 | 9.15-9.50<br />
Mix<strong>in</strong>g of high-Schmidt<br />
number scalar <strong>in</strong> regular/<br />
<strong>fractal</strong> grid turbulence:<br />
Experiments by PIV and PLIF<br />
Y. Sakai, K. Nagata, H. Suzuki, and R. Ukai<br />
Department of Mechanical Science and Eng<strong>in</strong>eer<strong>in</strong>g, Nagoya<br />
University, Japan<br />
<strong>Turbulent</strong> mix<strong>in</strong>g of high-Schmidt-number passive scalar <strong>in</strong> the regular and <strong>fractal</strong><br />
grid turbulence is experimentally <strong>in</strong>vestigated us<strong>in</strong>g a water channel. A turbulence<br />
generat<strong>in</strong>g grid is <strong>in</strong>stalled at the entrance to the test section, which is 1.5 m <strong>in</strong><br />
length and 0.1 m x 0.1 m <strong>in</strong> the cross section. Two types of grids are used: one<br />
is a regular grid of the square-mesh and biplane construction, and another is a<br />
square type <strong>fractal</strong> grid, which was first <strong>in</strong>vestigated by Hurst & Vassilicos [4] and<br />
Seoud & Vassilicos [5]. Both grids have the same solidity of 0.36. The Reynolds<br />
number based on the mesh size, Re M<br />
= U 0<br />
M eff<br />
/ν is 2,500 <strong>in</strong> both <strong>flows</strong>, where U 0<br />
is the cross-sectionally averaged mean velocity, M eff<br />
is the effective mesh size and<br />
ν is the k<strong>in</strong>ematic viscosity. A fluorescent dye (Rhodam<strong>in</strong>e B) is homogeneously<br />
premixed only <strong>in</strong> the lower half stream, and therefore, the scalar mix<strong>in</strong>g layers with<br />
an <strong>in</strong>itial step profile develop downstream of the grids. The Schmidt number of<br />
the dye is O(10 3 ). The time-series particle image velocimetry (PIV) and the planar<br />
laser <strong>in</strong>duced fluorescence (PLIF) technique are used to measure the velocity and<br />
concentration field. The results show that the turbulence <strong>in</strong>tensity <strong>in</strong> the <strong>fractal</strong><br />
grid turbulence is much larger than the one <strong>in</strong> the regular grid turbulence (See<br />
Fig.1), and the turbulent mix<strong>in</strong>g <strong>in</strong> the <strong>fractal</strong> grid turbulence is strongly enhanced<br />
compared with <strong>in</strong> the regular grid turbulence at the same Re M<br />
(See Fig.2). It is also<br />
found that the scalar dissipation takes place locally even <strong>in</strong> the far downstream<br />
region at M eff<br />
= 120 <strong>in</strong> the <strong>fractal</strong> grid turbulence.<br />
TUESDAY 29 MARCH 2011 | 9.50-10.25<br />
Aero-acoustic<br />
performance of<br />
<strong>fractal</strong> spoilers<br />
J. Nedic, B. Ganapathisubramani, J.C. Vassilicos<br />
Department of Aeronautics, Imperial College London, UK<br />
J. Boree, L.E. Brizzi, A. Spohn<br />
Institut P’, CNRS • ENSMA • Universite de Poitiers, FRANCE<br />
One of the major environmental problems fac<strong>in</strong>g the aviation <strong>in</strong>dustry is that of<br />
aircraft noise. The work presented here, done as part of the EU’s OPENAIR Project,<br />
looks at reduc<strong>in</strong>g spoiler noise whilst ma<strong>in</strong>ta<strong>in</strong><strong>in</strong>g lift and drag characteristics<br />
through means of large-scale <strong>fractal</strong> porosity. It is hypothesised that the highly<br />
turbulent flow <strong>generated</strong> by <strong>fractal</strong> grids, which have multiple-length-scales, would<br />
reduce the impact of the re-circulation region and with it, the low frequency noise<br />
it generates. In its place, a higher frequency noise is <strong>in</strong>troduced which is more<br />
susceptible to atmospheric attenuation and could be deemed less offensive to<br />
the human ear. A total of n<strong>in</strong>e laboratory scaled spoilers were looked at, seven<br />
of which had a <strong>fractal</strong> design, one with a regular grid design and one solid for<br />
reference. The spoilers were <strong>in</strong>cl<strong>in</strong>ed at an angle of 30 o . Force, acoustic and flow<br />
visualisation experiments on a flat plate were carried out, where it was found that<br />
the present <strong>fractal</strong> spoilers reduce the low frequency noise by 2.5dB. Results show<br />
that it is possible to improve the acoustic performance by modify<strong>in</strong>g a number of<br />
parameters def<strong>in</strong><strong>in</strong>g the <strong>fractal</strong> spoiler, some of them very sensitively. From these<br />
experiments, two <strong>fractal</strong> spoilers were chosen for a detailed aero-acoustic study on<br />
a three-element w<strong>in</strong>g system, where it was found that the <strong>fractal</strong> spoilers had a 1dB<br />
reduction <strong>in</strong> the sound pressure level and were also able to ma<strong>in</strong>ta<strong>in</strong> the amount of<br />
lift and drag <strong>generated</strong> by the w<strong>in</strong>g system.<br />
Figure 1 The streamwise evolutions of<br />
streamwise velocity fluctuation <strong>in</strong>tensity<br />
normalized by<br />
Figure 2 Instantaneous fluctuat<strong>in</strong>g concentration field at<br />
around x/M eff = 80 by the regular grid (left side) and the <strong>fractal</strong><br />
square grid (right side). Red: c = 0.3, Blue: c = -0.3.<br />
Note: M eff = 10 mm for the regular grid (left side),<br />
M eff = 5.68 mm for the <strong>fractal</strong> grid (right side)<br />
14 turbulent <strong>flows</strong> <strong>generated</strong>/<strong>designed</strong> <strong>in</strong> <strong>multiscale</strong>/<strong>fractal</strong> ways: fundamentals and applications<br />
turbulent <strong>flows</strong> <strong>generated</strong>/<strong>designed</strong> <strong>in</strong> <strong>multiscale</strong>/<strong>fractal</strong> ways: fundamentals and applications 15
FOURTH session | Flow design for applications<br />
Flow design for applications | FOURTH session<br />
TUESDAY 29 MARCH 2011 | 11.00-11.35<br />
<strong>Turbulent</strong> premixed<br />
flames <strong>in</strong> <strong>fractal</strong>-grid<strong>generated</strong><br />
turbulence<br />
N. Soulopoulos 1 , J. Kerl 1 , F. Beyrau 1 , Y. Hardalupas 1 , A.M.K.P.<br />
Taylor 1 and J.C. Vassilicos 2<br />
1<br />
Department of Mechanical Eng<strong>in</strong>eer<strong>in</strong>g, Imperial College London, UK<br />
2<br />
Department of Aeronautics, Imperial College London, UK<br />
TUESDAY 29 MARCH 2011 | 11.35-12.10<br />
A parametric study about<br />
the effect of <strong>fractal</strong>-grid<br />
<strong>generated</strong> turbulence on the<br />
structure of premixed flames<br />
T. Sponfeldner 1 , S. Henkel 1 , N. Soulopoulos 1 , F. Beyrau 1 ,<br />
Y. Hardalupas 1 , A.M.K.P. Taylor 1 , J.C. Vassilicos 2<br />
1<br />
Department of Mechanical Eng<strong>in</strong>eer<strong>in</strong>g, Imperial College London, UK<br />
2<br />
Department of Aeronautics, Imperial College London, UK<br />
Reactions between fuel and oxidiser take place at the molecular level, so turbulent<br />
motion at the smallest scales has an immediate effect on the process. We are<br />
concerned here with premixed combustion, where the fuel and the oxidiser are<br />
homogeneously mixed before react<strong>in</strong>g; spark-ignition <strong>in</strong>ternal combustion eng<strong>in</strong>es<br />
are a notable example of premixed combustion <strong>in</strong> applications. In the flamelet<br />
description of turbulent premixed combustion, the thickness of a lam<strong>in</strong>ar flame with<br />
the same fuel-to-air ratio rema<strong>in</strong>s relatively unaffected by the turbulence. A ma<strong>in</strong><br />
effect of turbulence is, through the stretch rate, to <strong>in</strong>crease the surface area of the<br />
flamelets and, thus, <strong>in</strong>crease the reaction rate.<br />
The parameters used to describe a premixed flame are the normalised turbulent<br />
fluctuations u’/s L<br />
where u’ is the rms of the turbulent fluctuations and s L<br />
is the lam<strong>in</strong>ar<br />
flame speed, and the ratio l/l F<br />
where l is the <strong>in</strong>tegral length scale and l F<br />
is the lam<strong>in</strong>ar<br />
flame thickness.<br />
<strong>Turbulent</strong> premixed flames are established <strong>in</strong> a square burner, where a regular<br />
square mesh grid and a space-fill<strong>in</strong>g <strong>fractal</strong> square grid are used to generate<br />
turbulence at various distances upstream of the flame stabilisation position, so<br />
different values of u’/s L<br />
and l/l F<br />
are obta<strong>in</strong>ed; 0.76 < u’/s L<br />
< 1.79 and 7.1 < l/l F<br />
< 11.8.<br />
The measurement techniques <strong>in</strong>clude OH* chemilum<strong>in</strong>escence and OH Planar<br />
Laser Induced Fluorescence (PLIF) which are used to measure the turbulent flame<br />
speed, the flame width, the <strong>in</strong>stantaneous flame front, the flame curvature and the<br />
flame surface density.<br />
The ma<strong>in</strong> result of the present measurements is that, at the same level of<br />
normalised turbulent fluctuations and similar <strong>in</strong>tegral length scales, the flames<br />
show larger turbulent flame speeds when us<strong>in</strong>g the <strong>fractal</strong> grid than when us<strong>in</strong>g the<br />
square grid. An attempt to expla<strong>in</strong> this difference relates to the different turbulence<br />
decay between normal- and <strong>fractal</strong> grid-<strong>generated</strong> turbulence.<br />
‘Fractal’ or <strong>multiscale</strong> turbulence-generat<strong>in</strong>g grids produce bespoke turbulent <strong>flows</strong><br />
<strong>designed</strong> for the particular application at hand [4]. They allow more design and<br />
optimisation flexibility than conventional turbulence generators like perforated<br />
plates, for example, and generate high turbulence <strong>in</strong>tensity at some distance away<br />
from the grid and over a long region downstream at a low pressure drop cost. This<br />
extended region of high turbulence <strong>in</strong>tensity and the fact that it is possible to design<br />
where this region starts and its overall extent are of great <strong>in</strong>terest for premixed<br />
combustion and may pave the way for future <strong>fractal</strong> combustors particularly adept<br />
at operat<strong>in</strong>g at the lean premixed combustion regime where NOx-emissions are<br />
the lowest. The high turbulence <strong>in</strong>tensity, <strong>in</strong> particular, <strong>in</strong>creases turbulent burn<strong>in</strong>g<br />
speed and leads to higher power densities of the flame. In previous work we<br />
observed a significant <strong>in</strong>crease of turbulent flame speed when us<strong>in</strong>g a <strong>fractal</strong><br />
<strong>in</strong>stead of a regular grid [12].<br />
In this work we further <strong>in</strong>vestigate the <strong>in</strong>fluence of <strong>fractal</strong>-grid <strong>generated</strong> turbulence<br />
on the structure of a premixed V-shaped methane-air flame. For a parametric<br />
study, a set of different space-fill<strong>in</strong>g <strong>fractal</strong> square grids is <strong>designed</strong> and several<br />
design parameters such as the blockage ratio and the ratio between the sizes of<br />
the largest and the smallest structures of the <strong>fractal</strong> grids are varied <strong>in</strong>dependently<br />
from each other. A regular square mesh grid with the same blockage ratio as two<br />
of the <strong>fractal</strong> grids acts as reference case. The velocity fields for the different grids<br />
are characterized based on hot wire measurements. The structure of the <strong>generated</strong><br />
flames is <strong>in</strong>vestigated us<strong>in</strong>g the conditioned particle image velocimetry technique<br />
[13]. Quantities like the flame brush thickness, flame surface density and the<br />
turbulent burn<strong>in</strong>g velocity as well as the flow field characteristics are compared.<br />
Prelim<strong>in</strong>ary results show significantly higher corrugation of the flames and larger<br />
flame brush thicknesses for all <strong>fractal</strong> grids.<br />
16 turbulent <strong>flows</strong> <strong>generated</strong>/<strong>designed</strong> <strong>in</strong> <strong>multiscale</strong>/<strong>fractal</strong> ways: fundamentals and applications<br />
turbulent <strong>flows</strong> <strong>generated</strong>/<strong>designed</strong> <strong>in</strong> <strong>multiscale</strong>/<strong>fractal</strong> ways: fundamentals and applications 17
FIFTH session | Simulations<br />
Simulations | FIFTH sessioN<br />
TUESDAY 29 MARCH 2011 | 13.30-14.05<br />
Turbulence<br />
modulation through<br />
broad-band forc<strong>in</strong>g<br />
B. Geurts<br />
Twente University, HOLLAND<br />
TUESDAY 29 MARCH 2011 | 14.05-14.40<br />
Direct Numerical<br />
Simulation of<br />
<strong>multiscale</strong> <strong>generated</strong><br />
turbulence<br />
S. Laizet, J. C. Vassilicos<br />
Department of Aeronautics, Imperial College London, UK<br />
E. Lamballais, V. Fortuné<br />
Institut P’, CNRS • ENSMA • Universite de Poitiers, FRANCE<br />
The response of turbulent flow to forc<strong>in</strong>g that is simultaneously imposed at a variety<br />
of length- scales is <strong>in</strong>vestigated numerically. This is a prime example of “modulated<br />
turbulence” <strong>in</strong> which a pre-specified departure from Kolmogorov turbulence is the<br />
target, e.g. to control mix<strong>in</strong>g-rates or emphasize certa<strong>in</strong> length-scales to stimulate<br />
embedded small scale chemical processes. We review the direct forc<strong>in</strong>g approach<br />
and discuss the response to time-modulated forc<strong>in</strong>g. Comparison is made with<br />
theoretical predictions. The occurrence of response maxima is presented and<br />
<strong>in</strong>terpreted <strong>in</strong> terms of experimental observations reported <strong>in</strong> literature. A central<br />
rema<strong>in</strong><strong>in</strong>g issue is the rigorous connection between the “modulat<strong>in</strong>g mechanism”<br />
and the associated broadband forc<strong>in</strong>g. In case the modulation is derived from flow<br />
through complex gasket-structures, the possibility offered by immersed boundary<br />
methods to represent the flow and the geometry <strong>in</strong> all their details, is discussed.<br />
Some simulation results for turbulent pipe flow, tripped by flanges derived from<br />
<strong>fractal</strong> geometries, are presented.<br />
Multiscale (<strong>fractal</strong>) geometry is a concept <strong>in</strong> which a given pattern is repeated and<br />
split <strong>in</strong>to parts, each of which be<strong>in</strong>g a reduced-copy of the whole. Multiscale (<strong>fractal</strong>)<br />
objects can be <strong>designed</strong> to be immersed <strong>in</strong> any fluid flow where there is a need to<br />
control the turbulence <strong>generated</strong> by the object. Experiments carried out at Imperial<br />
College London have shown that such objects can be used to control and manage<br />
the transition from lam<strong>in</strong>ar to turbulent <strong>flows</strong>. It was found that, unlike a regular<br />
object (where the turbulence is <strong>generated</strong> by only one scale), a slight modification of<br />
one of the object’s parameters can deeply modify the turbulence <strong>generated</strong> by the<br />
fluid’s impact on the object. Multiscale objects offer the opportunity to discover new<br />
complex flow effects/<strong>in</strong>teractions that can help understand how to control and/or<br />
manage complex fluid <strong>flows</strong>. Furthermore, such <strong>multiscale</strong> objects can be <strong>designed</strong><br />
as energy-efficient mixers, be <strong>designed</strong> to have a high sound transmission loss,<br />
be used around and/or <strong>in</strong>side build<strong>in</strong>gs <strong>in</strong> order to reduce the cost of heat<strong>in</strong>g and/<br />
or cool<strong>in</strong>g and therefore save energy (open<strong>in</strong>g vents, louvres, etc.) or be used to<br />
force drift<strong>in</strong>g of snow or sand to occur <strong>in</strong> a predictable place, rather than randomly.<br />
The experiments from Imperial College were performed without time for<br />
optimisation and adaptation. Hence, possibilities for improvement are considerable<br />
with the potential to set new <strong>in</strong>dustrial standards. However, the development of<br />
such new flow solutions cannot be br<strong>in</strong>g to fruition without a clear understand<strong>in</strong>g<br />
of the unique properties of <strong>multiscale</strong>-<strong>generated</strong> <strong>flows</strong>. It is clear that carry<strong>in</strong>g out<br />
experiments will help to tackle this ambitious task but will not be enough, even<br />
with advanced visualisation tools. It is absolutely necessary to undertake numerical<br />
simulations of such complex <strong>flows</strong>. In this work, these <strong>multiscale</strong>-<strong>generated</strong> <strong>flows</strong><br />
will be <strong>in</strong>vestigated us<strong>in</strong>g High Performance Comput<strong>in</strong>g (HPC) resources [14,15]. It<br />
provides an opportunity to understand their highly unusual properties and it will be<br />
very useful to propose high-quality standards of new technologies.<br />
18 turbulent <strong>flows</strong> <strong>generated</strong>/<strong>designed</strong> <strong>in</strong> <strong>multiscale</strong>/<strong>fractal</strong> ways: fundamentals and applications<br />
turbulent <strong>flows</strong> <strong>generated</strong>/<strong>designed</strong> <strong>in</strong> <strong>multiscale</strong>/<strong>fractal</strong> ways: fundamentals and applications 19
FIFTH session | Simulations<br />
Simulations | FIFTH sessioN<br />
TUESDAY 29 MARCH 2011 | 15.00-15.35<br />
LES of opposed jet<br />
<strong>flows</strong> employ<strong>in</strong>g<br />
<strong>fractal</strong> turbulencegenerat<strong>in</strong>g<br />
plates<br />
M. Pettit, S. Wysocki, P. Geipel, A. M. Kempf<br />
Department of Mechanical Eng<strong>in</strong>eer<strong>in</strong>g, Imperial College London, UK<br />
TUESDAY 29 MARCH 2011 | 15.35-16.10<br />
DNS on spatially<br />
develop<strong>in</strong>g <strong>fractal</strong><br />
<strong>generated</strong> turbulence<br />
with heat transfer<br />
H. Suzuki 1 , K. Nagata 1 , Y. Sakai 1 , T. Hayase 2<br />
1<br />
Department of Mechanical Science and Eng<strong>in</strong>eer<strong>in</strong>g, Nagoya<br />
University, JAPAN<br />
2<br />
Institute of Fluid Science, Tohoku University, Sendai, JAPAN<br />
Generation of fully developed, isotropic turbulence is essential for the entire<br />
range of <strong>in</strong>dustrial combustors, as it promotes the mix<strong>in</strong>g of react<strong>in</strong>g species and<br />
therefore improves efficiency <strong>in</strong> burn<strong>in</strong>g and reduces the emission of harmful waste<br />
products. However, such turbulence must typically be <strong>generated</strong> actively, which is<br />
often achieved by <strong>in</strong>corporat<strong>in</strong>g a swirl design. In laboratory experiments, block<strong>in</strong>g<br />
plates, grids or meshes, which are <strong>designed</strong> to encourage the transition from<br />
lam<strong>in</strong>ar to turbulent Large Eddy flow, Simulation are also of Opposed used. Jet Flows Employ<strong>in</strong>g Fractal Turbulence-<br />
Opposed jet configurations are widely Generat<strong>in</strong>g used Plates for the <strong>in</strong>vestigation of lam<strong>in</strong>ar and<br />
turbulent premixed [16], partially-premixed<br />
M. Pettit, S. Wysocki, P.<br />
[17]<br />
Geipel,<br />
and<br />
A. M.<br />
non-premixed<br />
Kempf<br />
flames [18]. The<br />
compactness of the flow doma<strong>in</strong> is of benefit to experimental and numerical studies<br />
Imperial College, Exhibition Road, London SW7 2AZ, UK, e-mail: a.kempf@imperial.ac.uk<br />
alike, while good optical access to the stagnation plane and flame is permitted<br />
Generation of fully developed, isotropic turbulence is essential for the entire range of <strong>in</strong>dustrial<br />
for the laser-based measurement techniques used to obta<strong>in</strong> two-dimensional<br />
combustors, as it promotes the mix<strong>in</strong>g of react<strong>in</strong>g species and therefore improves efficiency <strong>in</strong><br />
velocity and burn<strong>in</strong>g scalar and reduces data. the Through emission of the harmful use waste of products. a <strong>fractal</strong> However, turbulence-generat<strong>in</strong>g such must plate<br />
typically be <strong>generated</strong> actively, which is often achieved by <strong>in</strong>corporat<strong>in</strong>g a swirl design. In<br />
(Fig. 1) positioned<br />
laboratory experiments,<br />
downstream<br />
block<strong>in</strong>g<br />
of<br />
plates,<br />
the<br />
grids<br />
conventional<br />
or meshes, which<br />
perforated<br />
are <strong>designed</strong> to<br />
plate,<br />
encourage<br />
Geipel<br />
the<br />
et al.<br />
[19] report transition a significant from lam<strong>in</strong>ar <strong>in</strong>crease to turbulent flow, <strong>in</strong> are turbulent also used. Reynolds numbers achieved for the<br />
configuration, Opposed while jet configurations avoid<strong>in</strong>g are ext<strong>in</strong>ction widely used for of the the <strong>in</strong>vestigation flame of due lam<strong>in</strong>ar to and excessive turbulent premixed stra<strong>in</strong> rates<br />
at the stagnation [1], partially-premixed plane. [2] The and non-premixed <strong>generated</strong> [3] flames. turbulence The compactness has of been the flow shown doma<strong>in</strong> is of to be fully<br />
benefit to experimental and numerical studies alike, while good optical access to the stagnation plane<br />
developed and flame isotropic permitted near for the to laser-based the nozzle measurement exit techniques planes. used to obta<strong>in</strong> two-dimensional<br />
In the present<br />
velocity and<br />
work,<br />
scalar<br />
LES<br />
data. Through<br />
is used<br />
the use<br />
to<br />
of a<br />
acquire<br />
<strong>fractal</strong> turbulence-generat<strong>in</strong>g<br />
a more complete<br />
plate (Fig. 1)<br />
understand<strong>in</strong>g<br />
positioned<br />
of<br />
downstream of the conventional perforated plate, Geipel et al. [4] report a significant <strong>in</strong>crease <strong>in</strong><br />
the mechanisms turbulent Reynolds that provide numbers achieved this level for the of configuration, turbulence, while avoid<strong>in</strong>g by allow<strong>in</strong>g ext<strong>in</strong>ction of <strong>in</strong>spection the flame of the<br />
due to excessive stra<strong>in</strong> rates at the stagnation plane. The <strong>generated</strong> turbulence has been shown to be<br />
flow field development with<strong>in</strong> nozzles of the opposed jets (Fig. 2). Statistical<br />
fully developed and isotropic near to the nozzle exit planes.<br />
measures of first and second moments of flow velocity are obta<strong>in</strong>ed from simulations<br />
In the present work, Large Eddy Simulation is used to acquire a more complete understand<strong>in</strong>g of the<br />
and compared<br />
mechanisms<br />
to <strong>in</strong>-nozzle<br />
that provide<br />
measurements.<br />
this level of turbulence,<br />
Entirely<br />
by allow<strong>in</strong>g<br />
accurate<br />
<strong>in</strong>spection of<br />
representation<br />
the flow field<br />
of the<br />
complex plate development geometry with<strong>in</strong> the nozzles requires of the opposed grid resolutions jets (Fig. 2). Statistical typical measures of of first a Direct and second Numerical<br />
moments of flow velocity are obta<strong>in</strong>ed from simulations and compared to <strong>in</strong>-nozzle measurements.<br />
Simulation. Entirely The accurate study representation also aims of the to complex provide plate geometry a deeper requires <strong>in</strong>sight grid resolutions <strong>in</strong>to typical the of application<br />
a<br />
of the theory Direct upon Numerical which Simulation. the The study <strong>fractal</strong> also aims plate to provide was a deeper <strong>designed</strong>, <strong>in</strong>sight <strong>in</strong>to the and application may of potentially<br />
the theory upon which the <strong>fractal</strong> plate was <strong>designed</strong>, and may potentially suggest modifications or<br />
suggest modifications improvements that may or improvements be made to further improve that the may characteristics be made of the flow to with<strong>in</strong> further region improve the<br />
characteristics<br />
of the flame.<br />
of the flow with<strong>in</strong> the region of the flame.<br />
In recent years, fundamental characteristics of <strong>fractal</strong> <strong>generated</strong> turbulence (FGT)<br />
[4] are <strong>in</strong>vestigated experimentally. The most noteworthy characteristic of FGT is a<br />
constancy of the <strong>in</strong>tegral length scale <strong>in</strong> the streamwise direction [5]. In this work,<br />
we focus on the heat transfer <strong>generated</strong> by the constant mean temperature gradient<br />
[20, 21] <strong>in</strong> the FGT by means of direct numerical simulation. It is known that the<br />
temperature variance DNS on Spatially <strong>generated</strong> Develop<strong>in</strong>g by the mean Fractal temperature Generated Turbulence gradient exponentially<br />
with Heat Transfer<br />
<strong>in</strong>creases <strong>in</strong> the streamwise direction [20]. This streamwise evolution corresponds<br />
to an exponential <strong>in</strong>crease H. Suzuki of the 1 , K. Nagata large 1 , Y. scale Sakai 1 ,[20]. and T. Thus, Hayase 2<br />
it is worth <strong>in</strong>vestigat<strong>in</strong>g<br />
the streamwise evolution of the temperature fluctuation <strong>generated</strong> by the constant<br />
1 Department of Mechanical Science and Eng<strong>in</strong>eer<strong>in</strong>g, Nagoya University, Nagoya, Japan<br />
mean temperature gradient 2 Institute <strong>in</strong> of Fluid the Science, spatially Tohoku develop<strong>in</strong>g University, Sendai, FGT. Japan<br />
hsuzuki@nagoya-u.jp<br />
Direct numerical simulations based on the f<strong>in</strong>ite difference method is used for<br />
A BST R A C T<br />
analysis of the heat transfer phenomena <strong>generated</strong> by constant mean temperature<br />
In recent years, fundamental characteristics of <strong>fractal</strong> <strong>generated</strong> turbulence (FGT) 1 are <strong>in</strong>vestigated<br />
gradient experimentally. <strong>in</strong> the spatially The most noteworthy develop<strong>in</strong>g characteristic FGT. of FGT Our is a numerical constancy of the techniques <strong>in</strong>tegral length scale are <strong>in</strong> based<br />
streamwise direction<br />
on the numerical scheme 2 . In this work, we focus on the heat transfer <strong>generated</strong> by the constant mean temperature<br />
gradient 3,4 <strong>in</strong> the FGT by means developed of the direct numerical by Mor<strong>in</strong>ishi simulation. It et is known al. [22], that the which temperature enables variance us to<br />
<strong>generated</strong> by the mean temperature gradient exponentially <strong>in</strong>creases <strong>in</strong> streamwise direction<br />
perform DNS with analytically-expanded conservation of velocity 3 . This streamwise<br />
and temperature<br />
evolution corresponds to exponential <strong>in</strong>crease of the large scale 3 . Thus, it is worth <strong>in</strong>vestigat<strong>in</strong>g the streamwise<br />
fluctuations. evolution In of addition, temperature fluctuation higher <strong>generated</strong> order terms, by the constant i.e, mean viscous temperature and gradient diffusion <strong>in</strong> the spatially terms, were<br />
develop<strong>in</strong>g FGT.<br />
discretized Direct by numerical the higher-order simulation based on central the f<strong>in</strong>ite difference compact method schemes is used for analysis [23] of and the heat Fourier transfer series<br />
expansion. phenomena Figure <strong>generated</strong> 1 by shows constant mean the temperature streamwise gradient <strong>in</strong> evolutions the spatially develop<strong>in</strong>g of temperature FGT. Our numerical variance<br />
techniques are based on the numerical scheme developed by Mor<strong>in</strong>ishi et al. 5 , which enables us to perform DNS<br />
<strong>in</strong> the <strong>fractal</strong> with analytically-expanded and classical conservation grid turbulence. of velocity and temperature The fluctuations. temperature In addition, variance higher order terms, <strong>in</strong> classical<br />
i.e, viscous and diffusion terms, were discretized by the higher-order central compact schemes<br />
grid turbulence <strong>in</strong>creases exponentially. In contrast, that <strong>in</strong> FGT 6 and Fourier series<br />
expansion. Figure 1 shows the streamwise evolutions of temperature variance <strong>in</strong> the <strong>fractal</strong> and classical<br />
monotonically<br />
grid<br />
decreases turbulence. <strong>in</strong> downstream The temperature variance region, <strong>in</strong> classical where grid turbulence <strong>in</strong>creases is exponentially. decay<strong>in</strong>g. In contrast, that <strong>in</strong> FGT<br />
monotonically decreases <strong>in</strong> downstream region, where turbulence is decay<strong>in</strong>g.<br />
Figure 1: The <strong>fractal</strong> cross<br />
grid used <strong>in</strong> the present work.!<br />
Figure 2: The result<strong>in</strong>g <strong>in</strong>stantaneous axial velocity field with<strong>in</strong> a s<strong>in</strong>gle<br />
nozzle, correspond<strong>in</strong>g to section ‘A-A’ <strong>in</strong> Fig. 1. Blue dashed l<strong>in</strong>es<br />
<strong>in</strong>dicate positions of the perforated TGP and <strong>fractal</strong> cross grid.<br />
Figure 1 The streamwise evolutions of temperature variance <strong>in</strong> <strong>fractal</strong> (FGT) and classical (CGT) grid turbulence<br />
References<br />
1 D. Hurst and J. C. Vassilicos, Phys. Fluids 19, 035103 (2007).<br />
2 R. E. Seoud and J. C. Vassilicos, Phys. Fluids 19, 105108 (2007).<br />
20 turbulent <strong>flows</strong> <strong>generated</strong>/<strong>designed</strong> ! <strong>in</strong> <strong>multiscale</strong>/<strong>fractal</strong> ways: fundamentals and applications<br />
turbulent <strong>flows</strong> <strong>generated</strong>/<strong>designed</strong> <strong>in</strong> <strong>multiscale</strong>/<strong>fractal</strong> ways: 3 A. Sirivat and Z. Warhaft, J. Fluid Mech. 128, 323-346 (1983).<br />
fundamentals and applications 21<br />
References<br />
4 M. R. Overholt and S. B. Pope, Phys. Fluids 8, 3128 (1996).<br />
[1] Jones, W.P., Prasetyo, Y., Symp. (Int.) Combust. (1996) 26:275-282<br />
5 Y Mor<strong>in</strong>ishi, J. Comput. Phys. 143, 90-124 (1998).
References<br />
References<br />
[1] W.K. George, Advances <strong>in</strong> Turbulence, (WK George and REA Arndt, eds.), 1 - 42,<br />
Hemisphere Press, NY (now available from books.google.com). (1989)<br />
[2] W.K. George, 2008 Freeman Lecture, ASME Fluids Eng<strong>in</strong>eer<strong>in</strong>g Meet<strong>in</strong>g,<br />
Jacksonville, FL, USA, Aug. 10-14, 2008, ASME paper number ASME FEDSM2008<br />
-555362, (2008)<br />
[3] W.K. George & L. Davidson, AIAA 41st Aerospace Sciences Meet<strong>in</strong>g and<br />
Exhibition, Reno, NV, Jan. 6-9, 2003, AIAA paper number 2003-0064 (2003)<br />
[4] D. Hurst & J.C. Vassilicos, Physics of Fluids, Vol. 19, 035103. (2007)<br />
[5] R.E. Seoud & J.C. Vassilicos, Physics of Fluids, Vol. 19, 105108. (2007)<br />
[6] M. Oberlack & A. Rosteck, Discret. Cont<strong>in</strong>. Dyn. Syst. Ser. S 3(3), 451–471 (2010)<br />
[7] A. Rosteck & M. Oberlack, J. Nonl<strong>in</strong>ear Mathematical Physics (2011)<br />
[8] S. Hoyas & J. Jimenez, Physics of Fluids, Vol. 18, 011702 (2006)<br />
[9] S. Goto, Journal of Fluid Mechanics, Vol. 605, pp 355-366 (2008)<br />
[10] N. Mazellier & J.C. Vassilicos, Physics of Fluids, Vol. 22, 075101. (2010)<br />
[11] H. Suzuki et al, Proc. 6th Int. Symp. on Turbulence and Shear Flow Phenomena,<br />
Vol.1, pp.55-60 (2009).<br />
[12] N. Soulopoulos et al., Presented at the 33rd International Symposium on<br />
Combustion, Beij<strong>in</strong>g, Ch<strong>in</strong>a (2010)<br />
[13] S. Pfadler, F. Beyrau, A. Leipertz, Opt. Express Vol. 15, 15444 (2007)<br />
[14] S. Laizet, E. Lamballais & J.C. Vassilicos, Computers & Fluids, vol 39-3, pp<br />
471-484 (2010)<br />
[15] S. Laizet & N. Li, In Press <strong>in</strong> Int. J. of Numerical Methods <strong>in</strong> Fluids (2011)<br />
[16] W.P. Jones & Y. Prasetyo, Symp. (Int.) Combust. 26:275-282 (1996)<br />
[17] B. Böhm et al., Proc. Combust. Inst. 31:709-717 (2007)<br />
[18] M. Pettit et al, Proc. Combust. Inst. 33:1391-1399 (2011)<br />
[19] P. Geipel, K.H.H. Goh, R.P. L<strong>in</strong>dstedt, Flow, Turb. Combust. Vol. 85:397-419<br />
(2010)<br />
[20] A. Sirivat and Z. Warhaft, Journal of Fluid Mechanics, Vol. 128, 323-346 (1983)<br />
[21] M. R. Overholt and S. B. Pope, Physics of Fluids, Vol. 8, 3128 (1996)<br />
[22] Y. Mor<strong>in</strong>ishi, J. Comput. Phys, Vol. 143, 90-124 (1998)<br />
[23] S. Lele, J. Comput. Phys, Vol. 103, 16-42 (1992).