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TGS2015
International Short Course
New Theory on Turbulence Generation and
Sustenance in Boundary Layers
Chaoqun Liu Participants: Y. Wang, Y. Yan, P. Lu, L. Chen, X.
Liu, M. Thapa, H. Fu
University of Texas at Arlington
[email protected]
Tsinghua University, Beijing, China
June 4-6, 2015
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1. Your Goal, My Goal and Our Goal:
To reveal the secret of Turbulence, - a top mystery in
Nature
2. New Theory - may be more appropriate to call New Observations
or New Understandings as it is still on the developing stages and
many questions have
not been answered yet
3. Welcome questions, challenges and even criticisms
Let us work together to discover the physics of
Turbulence which bothers Human being for centuries. 4.Looking
for collaborations with Chinese scientists and students
5. Welcome to visit UTA with CSC Scholarship or apply UTA PhD
Program
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The Beginning of Systematic Studies of Laminar-Turbulent
Transition (FTT09)
Osborne Reynolds (1842-1912) Experimental Setup (1880)
Glass pipe
Glass-sided water tank
Introducing of
dye
Laminar-Turbulent Transition in Pipe Laminar-Turbulent
Transition in Pipe and Boundary-Layer
Laminar
regime
Transition to turbulence (normal lighting)
Aspect ratio is relatively small
Valve
Flow instability in transition region (lighting by electric
spark)
Reynolds Experimental (actually pipe flow is linearly
stable)
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These two types of flows are known to the most of us
empirically
Fist scientific observations of turbulence were performed,
perhaps, by Leonardo da Vinci (14521519)
While systematic investigations were started in the end of 19th
century only
Laminar and Turbulent Flows (FTT09)
Particle trajectories in laminar flow and in turbulent flow
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1. Introduction
Turbulence- top secret of nature
One of the most important unsolved problem of classical physics-
Richard Feynman (Nobel Prize Winner)
When I meet God, I am going to ask him two questions: why
relativity? And why turbulence? I really believe he
will have an answer for the first - Werner Heisenberg (Nobel
Prize Winner)
I am an old man now, and when I die and go to heaven there are
two matters on which I hope for enlightenment. One is quantum
electrodynamics, and the other is the turbulent motion of
fluids. And about
the former I am rather optimistic.
-Horace Lamb Famous British Scientist
http://en.wikipedia.org/wiki/Turbulence:
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A central unsolved problem of modern fluid dynamics
physical mechanisms of turbulence production and sustenance
New efficient turbulence models and (based on them) new simple
and reliable methods of prediction and control of transitional and
turbulent flows
Problem of Turbulence
Problem of Turbulence (FTT09)
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What Is Turbulence? Its Intuitive Understanding
Instead of Definition... .
Most of researches believe that turbulence is something that is
very:
complex (i.e. consisted of a great number of simpler
elements)
intricate, tangled (i.e. intensively mixing and also difficult
for understanding)
random (i.e. unpredictable, irreproducible, chaotic,
stochastic)
statistically stable (means turbulence is structured) (i.e. all
averaged characteristics statistics are very conservative)
In what sense the turbulence is random? No Is the turbulence
always unpredictable? No
Problem of Turbulence (FTT09)
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1. This phenomenon is essentially multi-stage
2. The objects of consideration are different at various stages
(external perturbations, instability modes, vortical
structures)
3. In general, this phenomenon is essentially nonlinear
4. There is a mixture of various disturbance scales in space, in
time, and in amplitude
Complexity of Turbulence Onset Problem Is Associated with
Several Reasons
Character of Transition and Classes of Instability (FTT09)
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Classical Transition Theory:
Main Stages of Transition Initiated by Three Classes of
Instability in Steady
Base Flows
x
(disturbance growth (disturbance growth in spacein space))
Convective InstabilitiesConvective Instabilities
x
(disturbance growth (disturbance growth in spacein space))
Convective InstabilitiesConvective Instabilities
t
Absolute InstabilitiesAbsolute Instabilities
(disturbance growth (disturbance growth in timein time))
t
Absolute InstabilitiesAbsolute Instabilities
(disturbance growth (disturbance growth in timein time))
Global InstabilitiesGlobal Instabilities
(growth (growth in space and timein space and time))
x
t
Global InstabilitiesGlobal Instabilities
(growth (growth in space and timein space and time))
x
t
Receptivity
Breakdown to Turbulence
Decay
Linear Instability
Decay
Nonlinear Instability
Ba
se
flo
w v
ari
atio
n Receptivity
Breakdown to Turbulence
Decay or Saturation
Linear Instability
Saturation
Ba
se
flo
w is fix
ed
Nonlinear Instability
Receptivity
Instability
Inversed Receptivity
Feedback
Disturbance
Saturation or Breakdown
Transition Scenarios Initiated by Different Classes of
Instability (FTT09)
Decay
Dominate in boundary layers
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Bypass
Morkovin (1984)
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Bypass Transition Scenarios
According to the original Morkovins (1968) definition all known
linear-instability mechanisms are bypassed in this case
After almost 40-years work in this field I have never seen a
transition process without stage of development of linear
instability. I am not sure that such case exist in nature
Moreover, it was shown theoretically by D. Henningson that only
linear-instability mechanisms are able to provide disturbance
growth in shear flows
However the term Bypass Transition is widely used and a lot of
people investigate this kind of transition scenarios!
The matter is that in the modern understanding the bypass
transition is the one initiated by non-modal linear instability
mechanisms (or by some other exotic linear instabilities)
Thus, the classical modal linear instability stage is bypassed
in this group of scenarios rather than linear instability stage at
all (as Morkovin assumed)!
Bypass
Morkovin (1984)
Normal, Bypass and Abrupt Transition Classes (FTT09,
Kachanov)
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2.2.4 Classical Theory - Copy from Lee 2004, Peking University,
China
Same theory can be found from many research papers and web
pages
Breakdown
Reconnection Unfortunately, breakdown and reconnection were not
observed by our DNS and theroretically
cannot happen!
Fig 3
Crow Theory
Breakdown to turbulence
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Copied from US National Research Center for Hypersonic
Laminar-Turbulence Transition Web Page
1.Turbulence is generated by linear and non-linear modes growth
and interaction?
2. Do we have vortex breakdown to get turbulent flow? That is
not the case
Current Transition Theory
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14
Figure 1: Jet experiment Figure 2: Photo of particle
movement
Figure 3: The vortex size in red circle is 11 micro meters and
the rotation speed is 6,000 circles/second
The size of vortex is around 10 to several hundred micro
meters
I (Liu) have addressed that the
nature of turbulence is that
fluid cannot tolerate shear and
shear, which is unstable, must
transfer to rotation, which is
stable. Turbulence is not
generated by vortex
breakdown which is incorrect
and misunderstanding. Cais experiment shows all particles
in turbulent flow is moving
forward (at about 0.544 m/s)
with fast rotation (around
10,000 circles/second or more)
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Vortices generated by water jet (Cais experimental observation
with highest resolution
of 1 , personal contact) m
How Fast is the Ring Rotation?
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What Is Turbulence?
My understanding:
Turbulent flow is a rotation dominant,
chaotic flow with different size of
vortices.
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By P. Roache, 1968
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Richardsons Ideas about Turbulence
- Classical
"Big whorls have little whorls that feed on their velocity, and
little whorls have smaller whorls and so on to
viscosity."
Lewis Fry Richardson (1881-1953)
This rhyme expresses poetically his idea of the turbulent
cascade:
1. Vorticity is created on large scales by some driving
mechanism that feeds energy to the fluid.
2. Shear instability causes smaller vortices to be
shed, drawing energy from the larger ones.
3. This process continues on ever smaller scales.
4. On the smallest scales, diffusion destroys eddies and
converts their kinetic energy to thermal energy.
Problem of Turbulence (FTT09)
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Richardsons vortex and energy cascade theory(1928) -
Classical
Fig 2(b)Sketch of Richardsons cascade process Frisch et al,
1978
Fig 2 (a) Sketch of Vortex breakdown
Feyhman,1955; Tsubota et al,2009
Big whirls have little whirls Which feed on their velocity;
And little whirls have lesser whirls,
And so on to viscosity in the molecular sense. Richardson
(1928)
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Richardson vortex cascade revisit
1. Why there is no one who can observe such an eddy cascade?
2. Why does one vortex break to two and then four, not three or
five?
3. Why does viscosity play role when the vortex size equals to
Re=1.
How about eddy Re=2, 4, 6 etc. where viscosity does not play any
role
at all?
As shown by our DNS, turbulence has different size of vortices
from
the large to the small. However, they are all generated by shear
layer
instability (K-H type) without exception and no vortex
breakdown is observed.
In fact, no one ever observed the eddy cascade by
instrument or computation as 3-D PIV is so advanced
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Kolmogorovs Turbulence
-Classical
Andrey Nikolayevich Kolmogorov (1903-1987) develops theory of
homogeneous, isotropic, incompressible turbulence based on
Richardson's ideas
Then it propagates from large-scale eddies, via
inter-mediate-scales to small-scale eddies. This range of inertial
scales is lossless.
Energy is added to the fluid at large scale lo
Main idea of Kolmogorovs Theory of Turbulence is: Turbulence
displays universal properties independent of initial and boundary
conditions
..
l1
l2
l0
inflow of energy
energy flux
energy dissipation Then it dissipats
as heat at small dissipative scale .
Problem of Turbulence (FTT09)
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Kolmogorovs Turbulence
Another Kolmogorovs assumption was that the spectral energy
distribution E(k) (where k=2p/l is vortex wavenumber) depends only
on energy flux and scale k. This was purely physical idea.
The same law is valid for frequency spectra because turbulent
vortices of the inertial range propagate downstream with almost
equal speeds (a flow velocity)
After that, it was easy to obtain famous Kolmogorovs formula
E(k)~2/3k-5/3 by means of dimensional theory only. This formula is
valid for inertial rage of wavenumbers.
k-5/3
Problem of Turbulence (FTT09)
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5.2 Kolmogorovs hypothesis revisit
Kolmogorov Hypothesis 1:
For very high Re, the turbulent motions with length scales much
smaller than L are statistically
independent of the components of the motion at the
energy-containing scales.
The energy-containing scales of the motion may be inhomogeneous
and anisotropic,
but this information is lost in the cascade so that at much
smaller scales the motion is locally
homogeneous and isotropic.
However, the hypothesis that the small length scale is universal
and isotropic is hard to
Prove by either DNS or experiment.
No one can prove the small eddies are universal and
isotropic.
Kolmogorov Hypothesis 2 (Kolmogorovs first similarity
hypothesis) For very high Re, the statistics of components in the
equilibrium range, being independent
of the larger scales, is universally and uniquely determined by
the viscosity
and the rate of energy dissipation
2 3 2
2( )
/ij ij
U U VS S
L U L
3 2 3 3 2 2 43 4
2 3 2 4
4 3 3/4
Re ( )
Re Re 1
,
( ) Re Re
U V U L V L L
L
UL Vand
Finally
orL L
For example, is , the smallest scale would be in each
direction.
We need grid points to resolve these small length scale , which
is impossible.
8Re 10610
L
18Re 10
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Kolmogorov Hypothesis 3 (second similarity hypothesis)
At very high Re the statistics of scales in the range 1 1L K
(called `inertial subrange') are universally and uniquely
determined by the scale k and
the rate of energy dissipation
Then, in the inertial subrange, the energy spectrum E(k) of the
turbulence must be of the form
2/3 5/3 1 1
0( ) ( )E k C k L k
where C is a constant. This is the famous `Kolomogorov's 5/3
law'
The energy spectrum versus wave number normalized by
the Kolmogorov scale is confirmed by experimental data
(Frisch, 1995). That is a great triumph of Kolmolgorov.
However, DNS can get same spectrum. On the other hand,
there are many reports about the spectrum of pressure
fluctuation which are discrepant from Kolmolgorovs dimensional
analysis.
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The serious weakness of classical theory given by Richardson
and Kolmogorof is that nobody ever observed. While Komogorovs
third hypothesis or (-5/3) spectrum law is proved correct (our DNS
is correct as well), Richardsons eddy cascade and breakdown,
Kolmogorov first (statistically isotropic for small
eddies) and second (Kolmogorov scales)hypotheses are never
confirmed. As a roughly estimate, we need 20 vortex breakdowns
to get
Kolmogorov scale, but we even cannot see a single one. As the
experiment
tools are so powerful and the visualization technology is so
advanced
nowadays, it is very hard to believe we still cannot detect the
vortex
breakdown process. The only conclusion we can believe is that
the
classical theory on turbulence generation may be not correct and
need to
be revisited.
Of course, we should not blame our older generations. They did
not have
either large scale computers or advanced experimental
instruments.
They had to rely on hypotheses. However, if we just simply
accept them
and teach our students in class without careful checking and
validation,
one generation by one generation, this would be our serious
mistake.
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Critical Questions 1. Turbulent flow is random and only has
statistic value meaningful
No, turbulent flow cannot be random should turbulent flow follow
conservation of mass, momentum and energy? Turbulence has coherent
structure
2. Turbulence is generated by large vortex breakdown No, vortex
cannot break down and turbulence cannot be generated by vortex
breakdown but shear layer instability
3. Large eddies give energy to smaller eddies through vortex
breakdown No, through the sweeps not vortex breakdown
4. Turbulence consists of Richardson eddy cascade and Kolmogorov
scales
No, Richardrson eddy cascade and Kolmogoriv small scales are
never confirmed.
5. Turbulence is generated by unstable linear modes through
absolute instability or
Convective instability
No, the linear modes are always small and cannot develop vortex.
The role of all
Modes is to trigger vorticity rollup from wall and generate
inflection points.
6. The nature of flow transition is that shear is unstable,
rotation is stable, the fluids
cannot tolerate shear and shear layer must transfer to rotation,
or laminar flow must
transfer to turbulent flow.
7. There is no such a process that Lambda vortex self deforms to
hairpin vortex. Vortex
Ring is not part of Lambda vortex. Lambda root and vortex ring
are generated separately
By different mechanism.
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Early Hairpin Vortex Models Theodorsen (1952)
Spanwise Vortex Filament Perturbed Upward (Unstable) - Vortex
Stretches, Strengthens, and Head Lifts Up More (45o)
Modern View = Theodorsen + Quasi-Streamwise Vortex
Short Review by Moin (2010)
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Streaks Lift-Up and Form Hairpin
Hairpins Inclined at 45 deg. (Principal Axis)
First Evidence of Theodorsens Hairpins
Re = 1700
Short Review by Moin
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Streaks Lift-Up and Form Hairpin
For Increasing Re, Hairpin Elongates and Thins
Streamwise Vortex Forms the Hairpin Legs
Short Review by Moin
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Forests of Hairpins Perry and Chong (1982)
Theodorsens Hairpin Modeled by Rods of Vorticity - Hairpins
Scattered Randomly in a Hierarchy of Sizes
Reproduces Mean Velocity, Reynolds Stress, Spectra - Has
Difficulty at Low-Wavenumbers
Short Review by Moin
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Packets of Hairpins Kim and Adrian (1982)
VLSM Arise From Spatial Coherence of Hairpin Packets
Hairpin Packets Align & Form Long Low-Speed Streaks
(>2)
Short Review by Moin
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Packets of Hairpins Kim and Adrian (1982)
Extends Perry and Chongs Model to Account for Correlations
Between Hairpins in a Packet; this Enhanced Reynolds Stress Leads
to Large-Scale Low-Speed Flow
Short Review by Moin
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Velocity and Stress
of Laminar and Turbulent
Flow (Adrian 2007)
Turbulence increases
velocity near the bottom
but decreases in the middle.
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Velocity Distribution in a transitional boundary layer
(turbulent boundary layer
Is similar) largest velocity and Reynolds stress are below the
displacement thickness where U>1.0
How to model ? Eddy Viscosity Model No Scientific Foundation
Be very careful with the distribution of turbulent
boundary layer!! 1.0
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Velocity Distribution
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Pre 1961 Development of Hot-wire anemometry & measurement of
statistical
properties.
1960s Visualization identifying organized (coherent) structures
related to
turbulence production.
1970s Conditional sampling and averaging methods (quadrant
analysis, VITA,
etc.) developed to quantify properties and effects of organized
structures.
1980s First DNS of turbulent channel and boundary layer flows
providing full
spatial field properties and access to 3D structural
information. First
experimental measurements of velocity gradient tensor based
properties:
vorticity, dissipation rate, etc.
Landmarks of Turbulent Boundary Layer Research
36
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37
1990s Development of better methods to identify vortices.
Implementation of
planar PIV providing new insights to flow structure. Development
of field
sites for experiments in the ASL at very high Reynolds
numbers.
Development of high Reynolds number laboratory facilities.
2000s DNS at significantly higher Reynolds numbers and
supersonic Mach
numbers. Use of stereo-, tomographic- & holographic-PIV to
provide
additional insight about flow structure.
2010s DNS for much higher Reynolds numbers and hypersonic flow
(Re ~ 11,000 & Mach ~ 12).
Landmarks of Turbulent Boundary Layer Research Contd
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38
XIAOHUA WU and PARVIZ MOINProfessor, Director Center for
Turbulence Research, Stanford University
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39
Dan Henningson, Professor, Director,
Swedish e-Science Research Centre, KTH Mechanics
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Transition in Boundary Layer Flow over Flat Plate
40
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41
Transition in Boundary Layer Flow over Flat Plate Contd
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42
Turbulent Boundary Layer
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43
Turbulent Boundary Layer Contd
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44
Turbulent Boundary Layer Contd (Jets)
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46
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Summary of Some of Adrians Work (Adrian 2007, best citation of
Phys &Fluids) 1. Quasi-streamwise vortices, hairpin vortices,
packets of hairpins are prevalent
2. Quasi-streamwise vortices and associated streaks
(Robinson)
3. Hairpins in packets auto generation mechanism 4. Lifted
hairpins detached 5. Multiple level vortex packets
6. Growth of packets mechanism of transport vorticity, low
momentum, turbulent kinetic energy
Major Differences of Our Theory:
1. They saw them, we saw them, all DNS people saw them, but we
answer
WHY. This also indicates we cannot be wrong! No chance!
2. Streaks instability is really shear layer instability (K-H
type)
3. We believe hairpins in packets are generated by shear layer
instability and
ring vortex stretch. We do not believe the auto-generation
mechanism
4. Lifted hairpin is never attached and detached from its
generation (Omega-
shape)
5. Multilevel vortex packets are not independent and they are
mothers and
sons due to sweeps which generate new shears
6. Energy transfer for multiple level packets are through vortex
ring sweeps and
new shear layers not vortex breakdown We believe no vortex
breakdown and shear layer instability is the mother of
turbulence
7. Hairpin leg and head are generated separately with different
mechanism:
Leg, ejection, low speed zone, shear layer, new rings
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Summary made by Wallace 2011
1. There has been remarkable progress in turbulent boundary
layer
research in the past 50 years, particularly in understanding the
structural
organization of the flow. Consensus exists that vortices drive
momentum
transport but not about the exact form of the vortices or how
they are
created and sustained. (We try to give the answers!!)
2. This progress has been fueled by developments in
experimental
instrumentation (multi-sensor hot-wire anemometry and PIV) but
most of
all with the advent of DNS in the 1980s and its subsequent
advances.
3. Further progress has been made by the development of high
Reynolds
number laboratory facilities and the use of field sites to study
the very
high Reynolds number atmospheric surface layer under near
neutral
stability conditions.
4. Challenges for the future:
- Incorporating the knowledge of the structure of turbulent
boundary
layers into models, including RANS and subgrid scale LES
models.
- Further extending the knowledge gained for zero pressure
gradient,
smooth wall boundary layers to the complexities of accelerating
and
decelerating boundary layers and flows with rough walls.
- Continuing to develop and implement methods to control
turbulent
boundary layers that occur in real engineering applications.
We try to give the answers!
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Recent Development A Short Review 1. Importance
Flow transition is Important to fundamental fluid dynamics and
flow control
2. Current Status
2.1 Linear instability and weekly non-linear instability have
been well understood (Kachanov, FTT09, 2009, Kachanov, 2003)
2.2 Non-linear stability especially late stages of flow
transition have not been well
understood (Kleiser et al, 1991; Sandham et al, 1992; U.Rist et
al 1995,
Borodulin et al, 2002Bake et al 2002, Rist et al, 2002;
Kachanov, 2003) 2.3 New Experimental studies (Guo et al, 2010)
2.4 DNS and LES studies (Liu, 1995, 1997; Rist et al 2002, 2004;
Lessure 1996; Wu
& Moin 2009) Wu and Moin (2009, Stanford university)
reported a new DNS for flow transition on a flat plate. They
obtained fully developed turbulent flow with a structure of
forests of ring-like vortices by flow transition at
zero pressure gradients. However, they did not give the
mechanism of the late flow transition. The
important mechanism of boundary layer transition such as sweeps
and positive spikes etc. cannot be
found from that paper.
2.5 Many questions have not been answered and many mysteries
have not been
revealed especially for late flow transition stages. Wallace
(2011): the exact form
of the vortices or how they are created and sustained is still
unknown (We are
Answering)
3. Our new DNS study (1920x128x240, t=0-30 T starting from 2009)
is targeting at
turbulence generation and sustenance a top mystery in nature
University of Texas at Arlington-Chaoqun Liu
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Let US Take a Break!
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Self-Contradictions of Current Flow Transition and Turbulence
Theory (Note that one counterexample is enough to overthrow a
theory and we really do not need the second example)
Chaoqun Liu, Yonghua Yan, Yiqian Wang
Department of Mathematics, University of Texas at Arlington,
Arlington, Texas 76019
53nd AIAA Aerospace Sciences Meeting, 5-9 January 2015,
Kissimmee, Florida,
USA
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52
1. Breakdown and Coherent Structure
Transition Community:
Turbulence is caused by vortex breakdown to countless pieces
Turbulence Community:
Turbulence has coherent structure
After the house collapses and breaks down to hundreds of
debris, can we believe the house still has structure ?
Does this house still have structure?
If the turbulence community is correct,
the transition community must be wrong
and vice versa. There is no possibility that
both are correct
Answer: Flow vortex structure never
breaks down
-
53
2. Helmoholtz Vorticity Conservation
Our fluid mechanics books say Helmoholtz vorticity
conservation
law must be satisfied and vortex tube cannot break down and
vortex tube must end at the boundary and cannot end inside
of the flow field.
Then the books and research papers say:
1.Turbulence is generated by vortex breakdown
2.Lambda vortex detached from the wall
3.Hairpin vortex breakdown and then reconnect
4.Bridge is formed to link lambda vortex legs
Can these statements be correct while directly violate
Helmoholtz
Law?
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Existing Theory on Hairpin Vortex Revisit
54
Figure 2. Hairpin vortices in Classical Theory
(Book Turbulence by xxxxx, 2004)
In classical view, legs of hairpin vortex are
placed on the wall surface (V=0) and the ring
head is located almost near the inviscid area
(V=1.)
Vortex tube must break down (Can tube break
down???.)
Directly Violate
Helmoholtz Vortex
Conservation Law
V=1 (170 m/s)
V=0
-
3. Is Lambda Vortex a Vortex Tube?
55
If it is true, vortex must break down
as top v=1 and bottom v=0 directly violate Kevin-Helmholtz
vorticity
conservation
1) Is Lambda vortex attached on the wall?
V=0? No, never attached, v is small but
not zero and becomes bigger when rolls up
.
2) Is Lambda vortex a vortex tube? No, it
Is a congregation of vorticity with a rotation
core (vortex tube cannot be penetrated by
vorticity lines)
A misunderstanding by using
V=1
V=0
2 iso serface
-
4. Lambda Vortex Self-deforms to Hairpin Vortex??
56
Does Lambda vortex self-deform to hairpin vortex?
No, nothing can self-deform. Deform is a
motion and motion needs force (dynamics)
Self deform?? Leg is formed by vorticity rollup and ring is
formed
by shear layer instability, ring and leg are separated
(xxxxx, 1986)
-
57
4B. Vortex Ring Formation (shear layer instability)
Low speed zone
Shear becomes rotation Multiple ring formation
-
58
5. Is Lambda vortex detached or attached on the wall?
1) First attached and then detached? (xxxxx 2007)
2) Vortex breaks down and then reconnects? (xxxxx 2002)
3) Bridges formed to link two legs? (xxxxx, 1996)
No mechanism to support the above
statements which directly violate vorticity
conservation law
Answer: Vortex never attached on the wall
-
59
5. We Have No Rigid Definition for Vortex
If we agreed, we then would have no serious research on
physics of turbulence
Vortex we defined is not a vorticity tube but a rotation
core
How fast of the rotation? 1,000-100,000 circles/per second
(According to Experiment and DNS)
-
60
6. Does Vortex Break Down? Never happens
Either vortex tube or rotation core (stable) cannot break
down
and we can make faked vortex breakdowns (xxxxx 1996) as
many as we wishby selecting an inappropriate 2 with same DNS
data
Vortex breakdown? No breakdown with same data
but different 2
-
61
6B. Faked Vortex Breakdown
Same Data Set but
Different Lambda2
-
62
7. Richardson Energy Cascade and Kolmogorov Vortex Breakdown
- No one found, why?
Vortex breakdown and eddy cascade no one found
What we found is that:
multiple level sweeps,
ejections, shear layers,
low speed zones,
lambda vortex and rings
-
Traditional Concepts (Sketch) Looks like unstable modes caused
transition (find eigenvectors and eigenvalues, if great than 1,
flow breaks down to become
turbulent? No, no, no, no such things and turbulence has strict
structure, step by
step.
Unstable modes, Linear, Non-linear, Breakdown
Absolutely Unstable?
0 0 0 0x x x x x
0 1 2 3x x x x x
Unstable modes, Linear, Non-linear, Breakdown
Convectional Unstable?
Turbulence is caused linear growth, nonlinear interaction and
resonance
of unstable modes - No
-
Linear Analytic Solution Is Same as DNS at Very Beginning?
No
DNS
Linear
spanwise vorticity
.)()('')(
33
)(
223232 ccezAezAqqqqq
yxti
dd
xti
dddddd
Linear solution is a wave solution and has nothing to do with
turbulence
generation or structure Turbulence has certain structure!!
-
There is no vortex formation in linear analytic solution -
Never
DNS
Linear
Distribution of w/x at z=10.95
Linear unstable modes cause transition? No (no vortex
formed)
-
66
8. Is Turbulence Generated by Linearly Unstable Modes? No
Like dust, gust, sand, fly, mosquito, all can trigger
turbulence.
The role of T-S waves or others induce vorticity rollup from
wall.
The nature is that fluid cannot tolerate shear (unstable
conditionally)
and shear must transfer to rotation (turbulence) which is stable
It is hard, If not impossible, to get success by suppression of
linear modes. Is anyone
sucessful in sppression of linear modes for aircraft design We
can burn the wood to make bread.
Can we say bread is made by wood not
flour? What makes bread? Wood or flour?
We may think linear modes are wood,
turbulence is bread, and Blasius profile is
flour. Shear to rotation transfer is the nature
of turbulence generation, not unstable modes
Absolute or convective instability or breakdown
cannot cause transition and cannot make turbulence!
-
Can mode suppression be successful? Hard if not impossible
1. Roughness study or control?
Does roughness have linearly unstable modes? No.
Is linear solution same as DNS? No. If not, why do linear
analysis
for roughness?
Roughness is nonlinear and the separation behind roughness
(if higher than the laminar sub-layer) to cause rollup
(we studied this 25 years go)
2. Unstable mode suppression?
Like wood burning can make bread, but bread is not made by
wood, linear unstable modes can promote turbulence
generation, but dust, gust, sand, flies, mosquitoes, etc can
as well. Key issue is to control vorticity rollup
-
68
Nature of Turbulence (shear must transfer to rotation)
u1
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
-2 -1 0 1 2
u1
Velocity of base flow Eigenvector
210 0
21
0 021
)()(
:
)()(
:
:Re
UUdydy
ydUdy
dy
ydU
onConservatiVorticity
dyyUdyyU
onConservatiMass
lation
-
510 s
51/ 0.85 10 /ref T s
4_ / 6.28 1.354 10 /refR ref circles s
max
5
max
3 5
12.0
1.624 10 / sec
0.78 2.5 340 / (1.21 4 10 ) / s 1.37 10 /
ref
gen
Rotation circles ond
Ring s
1. Characteristic Quantity:
Length: H=4 mm
Velocity: V=340 m/s
Time: T=H/V=1.1765
Angle Speed:
Rotation:
2. Our MVG Case:
Qualitatively Confirmed by Experiment of Lu et al (2010) and Cai
et al (2014)
MVG generate :
How Many Rings and How Fast Is the Rotation of the Vortex
Rings?
!!!
5 51.37 10 / sec , 1.624 10 / secvortex rings ond rotating with
circles ond
-
70
9. Bursting and Turbulence Intermittence Never Happen A
misunderstanding of vortex package motion
Can turbulence suddenly burst and then suddenly disappear -
Manipulated by God? No
This is a misunderstanding of vortex package self and relative
motion
by fixed hotwire or watching fluid particle motion in a fixed
Euler frame.
Turbulence disappear? Bursting ? Disappear again?
Intermittency?
Hotwire
-
71
Observation Station
-
What is fluctuation? turbulence bursting? Intermittence? -
Uneven vortex package is moving
Experiment Reproduce by our DNS
Measured by Kachanov
-
Figure 7. The velocity trace of the probe in a single
intermittence cycle while the blue points indicate the time
we
will be interested
Reynolds
-
Figure 8. The probe at z=2.41
with slice contoured by
pressure at consecutive times.
respectively corresponding
to the blue points in figure 7.
-
Helmoholtz particle velocity decomposition revisit
( ) ( )
1 1 1( ) ( ) ( )
2 2 2
1,
2
T T T
V X dX V X dV
dV dX V
V V V V V V V
dV dX dX where V
V
2
1 Is vorticity which does not mean rotation
(vorticity is not vortex or rotation)
0 VIrrotational Flow
0 VRotational Flow?? No
Could still be irrotational like Blasius solution
Should be further decomposed to rotational vorticity
and irrotational vorticity
Decomposed to deformation and rotation Serious
misunderstanding
Fluid motion: Translation, Deformation, Rotational Vorticity,
Irrotational Vorticity
( ) (1 )V R V R V V
In general R V
-
(Vorticity) (Vortex)
Is vortex vorticity or vorticity tube?
No, vorticity line cannot penetrate vortex tube
It is a serious mistake to consider vortex as vorticity tube or
vortex tube
(see Davidsons book)
-
1) vortex lines for lambda vortex
2) vortex lines for lambda vortex with lambda 2
Lambda is a rotation center not vortex tubes as vortex filaments
penetrated Lambda all times
3, Is Lambda vortex a vortex tube?
Lambda vortex should be Lambda Rotation Cores
-
Late stage of the development of vortex lines for 1st ring
Vortex filament
from neighboring
boundary layer
Later time steps:
filaments are stretched
and become longer
4, First vortex ring
-
My Velocity Decomposition
Assume A represents the velocity gradient tensor:
1 1( ) ( )2 2
1 1( ) ( )
2 2
1 1( ) ( )
2 2
1(
2
T TA V V V V V
dV V dl S dl V dl
Deformation Vorticity
u u u u u v u w
x y z x y x z x
v v v v u v v w
x y z x y y z y
w w w w
x y z
1 10 ( ) ( )
2 2
1 1( ) 0 ( )
2 2
1 1 1) ( ) ( ) ( ) 0
2 2 2
1 10
2 2
10
2
z y
xx xy xz
yx yy yz z
zx zy zz
u v u w
y x z x
u v v w
y x z y
u w v w u w v w
x z y z z z x z y
S S S
S S S
S S S
111 222 333 123 231 312
132 213 321
1 1
2 2
1 10
2 2
, , 1,2,3; : 0; 1;
0
1; 1 1 4
1 1 2
x ij ijk k ij ij
y x
ijk
ijk
S S W
where i j k
i j
or j i or i
j i or i
-
1 2 3, , 1 2 3
3 2
1 2 3 1 2 2 3 3 1 1 2 3
3 2
1 2 3
2 2 2 2
1 2 2 3 3 1 1 2 3 1 2 3
2
| | ( ) ( )( ) 0
( ) ( ) 0
0
: 0
1 1( ) ( ) ( )
2 2
10 ( )
2ij ji
A I
or
P Q
For incomprssible flow P
Q
Trace A a a
1
2V
Assume A has 3 distinct eigenvalues :
Q is an invariant
Vorticity is an invariant as well
21 1
2 4
1
2
ij ji ij ji
ij ij ijk k
Q a a S S a b
A S W or a S
Then both a and b are invariants
-
( ) (1 )V R V R V V
In general R V
V
; 0, 1, , ,
, min
ba no dissipation pure rotation stable
a b
a b deformation do ant
Vorticity does not mean rotation and should be further
decomposed
to rotational vorticity and irrotational vorticity
represents rotational voticity.
is another invariant
Let
( ) (1 )V R V R V V
In general R V
-
( ), 0u u z v w
2 2
2 2
1 1: ( )
2 2
1 1 1[ ( )] ( )
2 2 8
1 1 1[ ( )] ( )
4 2 16
10.333
3
y
u w uSpanwise vorticity
z x z
u w ua
z x z
u w ub
z x z
b
a b
For example, 2-D laminar boundary layer like Blasius
solution,
0 1.0a and then
There is no rotation for Blasius solution although the
vorticity
is very large near the wall
For vortex ring (pure rotation),
There is no dissipation.
We said rotation is not vorticity, why you use vorticity to
calculate
Actually, we use b to find
When the flow becomes rotation, b or deformation is reduced
and eventually becomes zero (stable) .
-
Calculation of rotation ratio
For a 2-D case
1 1( ) ( )
2 2
:
1 1( ) 0 ( )
2 2
1 1( ) ( ) 0
2 2
10
2
10
2
T T
yxx xz
zx zzy
A V V V V V
in a x z plane
u u u u w u w
x z x z x z x
w w u w w u w
x z z x z z x
S S
S S
1
2
0
, 1,2; 1 ;
1
ij ij y ij ij
ij y
S S W
i ju w
where i j i jz x
i j
100
0 0
0
y
princ
y
ij ji
aPAP S W B
b
S W
1 2
2
1 2 1 2
2
( )( ) 0
( ) 0
0
or
P Q
2 21 1 1 1 1( )( ) 0 02 2 4 2 4
ij ij ji ji ij ji y ij ji yQ S W S W S S S S
21 1 ,2 4
ij ji ya S S and b then Q a b
; 1b
thena b
Pure rotation
~
refQQQ
||
||
1 1[ ( ) (1 ) )]
2 2dV V dl S dl dl V S dl dl V V
222
zyx For 3-D
Represents vorticity rotational ratio, but independent to
vorticity strength
-
Figure 4 Vortex Structure by Lambda 2 Figure 5 Vortex
Structure
by Filtered Omega (Omega=0.5)
Figure 6 Original Omega iso-surface ( Omega=0.5)
There are clouds (may be physical), but vortex structure below
cloud is same
-
Vortex Identification
1. It is still a challenge how to visualize the vortex structure
in
a fluid flow field
2. Experiment limited capability for instantaneous flow 3.
Vorticity large on the wall surface 4. Lambda2 or Q-criteria It is
iso-surface and adjustable 5. Vortex filaments not very organized
6. Our method Combination of and selected vortex
filaments (not vorticity lines) for physics
-
Some Vortex Identification Methods: 1. Complex eigenvalues of
Criterion (Chong & Perry, 1990)
The rate-of-strain tensor is dominated by the rotation tensor.
This means
has complex eigenvalues (deformation tensor is symmetric
has complex eigenvlues
is positive
2. Q-criterion (Hunt, Wray and Moin, 1988) for incompressible
flow:
u
u
)||||||(||2
1
2
1)()(
2
1
)]()[(2
1)(
2222
3
2
2
2
1
2
3
2
2
2
1
2
321133221
SuuuTrace
Q
jiij
0)(23 uDetQP
23 )](2
1[)
3
1( uDetQ
The criterion is thQQ thQ Is some positive threshold
)(|||| 2 ttr Q is more positive, the rotation is stronger
-
ij ij ijA S W
21 1 1
2 2 4
1 1 3( )
3 3 4
ij ji ij ji
ij jk ki ij jk ki i j ij
Q A A S S
R A A A S S S S
Since , Q and R can be rewritten:
In general, there is both strain and vorticity. Q gives a
measure of relative intensity of the two. Large negative Q
indicates regions of strong strain and large positive Q marks
regions of intense enstrophy (rotation). If we specify certain
positive Q-criteria, the iso-surface of Q may give a rotation
center where 2
ij jiS S
.
-
1.Numerical post processing by 2 - criteria (Jeong &
Hussain, 1995)
The idea is still to find the local pressure extrema (minimum)
since in
general a strong rotation center should have a local pressure
minimum.
, , ,
1i j ij i jkka p u
,
ij ij
i j ik kj ik kj ik kj ik kj
DS Da S S S S
Dt Dt
, ,
1 ijij ij kk ik kj ik kj
DSp S S S
Dt
is the acceleration gradient and the
subscript comma means partial derivative
decomposed into symmetric and anti-
symmetric parts which is vorticity
transportequation and zero here.
Combine the above two
2 2S
We would not consider the first term and second term of the
right hand side since the first term represents unsteady straining
and the second term represents viscous effects. Then there is
only
to determine the local pressure minimum
-
Some Vortex Identification Methods: 3. - Criterion (Jeong &
Hussain, 1995) more negative, stronger rotation
Vortex core has local minimum pressure. Neglecting time
derivative and
Viscous effects,
Will be minimum when two of
The three eigenvalues are negative
Note that
4. My Criterion: (Liu & Wang 2015)
2
)(~1
, kjikkjikij SSp
2
4
1
2
1;5.0 ijiij bandSSa
ba
b
3212 0 if
p~
kjikkjikSS
Is symmetric
Advantages: 1) physical meaning is clear, pure rotation
2) Is not case-related like a threshold (we really do not know
why Q=4000?)
3) Does not ignore the weak vortex
1
5.0
-
Figure 4. Iso-surfaces of in (a) and (b) while
in (c)
in (c)
Figure 6. Iso-surfaces of
-
Figure 5. Iso-surfaces of (no filter) 52.0
-
LAMBDA
Figure 12. A vortex line contoured by vorticity magnitude
Figure 13. (a) The origination points of the five vortex
filaments; (b) The -vortex with the five vortex lines
0.8
0.4
-
Figure 13. (a) The origination points of the five vortex
filaments; (b) The -vortex with the five vortex lines
-
Table 3. The 3D velocity gradients of the first ring-like vortex
at successive four time steps
Table 2. The pseudo 2D velocity gradients of the first ring-like
vortex at successive times
Tensor Analysis for the First Vortex Ring (No rotation to fast
rotation, but vorticity does not increase much)
-
95
10. Multiple Vortex Rings Are Auto-generated? (xxxxx, 2007)
-Nothing can be auto-generated and must be under
certain mechanism
Multiple vortex rings are generated by shear layer
instability
11. Non-symmetry and chaos are auto-generated? (xxxxx 2007)
- Nothing can be auto-generated and must be under
certain mechanism
Non-symmetry is generated by instability of multiple level
vortex packages starting from the second level.
12. Can bifurcation of dynamic system is the mechanism of
Chaos of turbulence (xxxxx)? No
Navier-Stoke equation is not a dynamic system. They are
not related.
-
96
If flow transition is caused by linear modes and must
experience the process of self-deform from Lambda
vortex to hairpin vortex and breakdown, how to explain
bypass transition and free stream turbulence?
Anyway, the classical and current turbulence theories
are fully filled with self-contradictions.
Bypass Transition and Free Stream Turbulence
-
Helmoholtz Velocity Decomposition ( ) ( )
1,
2
V X X V X dV
dV dX dX where V
1 1
( ) ( )2 2
U u u v u v
y y y x y x
(a) Blasius solution (b) Pure shear (c) Pure rotation
Real Reason of Flow Transition (Blasius Solution)
0, 0,v
On surface vx
Bottom layer is always stable (shear cannot be rotation)
: ( ) ( )v
In field Shear unstable Rotation stablex
Internal Property of Fluid
-
Linear Analytic Solution Differs from DNS at Very Beginning
DNS
Linear
spanwise vorticity
.)()('')(
33
)(
223232 ccezAezAqqqqq
yxti
dd
xti
dddddd
-
There is no vortex formation in linear analytic solution -
Never
DNS
Linear
Distribution of w/x at z=10.95
Linear unstable modes cause transition? Never
-
DNS Differs from Linear Analytic Solution middle
-
Figure 12. Profiles of velocity derivatives (Uzz, Uzzz)
Figure 10. Velocity derivative (Uz, DNS on right)
-
Linear Modes Push Up the Vorticity from the Wall Change the
velocity Profile and generate the inflection points
Streamwise velocity and its derivative profile(Uz) x=418 in
Then what happens? Shear transfers to rotation vortex formed
by flow property of
shear transfer to rotation
not by unstable modes
-
Spanwise Vortex Lambda Vortex Root Vortex Ring
-
How to Predict and Control Flow Transition
1. N-Factor ? - No scientific foundation
2. Control the linear unstable modes?
Any thing which causes the vorticity rollup would cause flow
transition since this the flow property and not related to
any
unstable modes
Control or reduction of the linear unstable modes may be
useless.
3. Suggestions Control the shear layer formation, shape,
direction. Shear layer instability is mother of turbulence
not the unstable modes
-
Lius early DNS work on flow transition in 1995
-
Lius early DNS work on high speed flow transition in 1997
-
Lius Recent DNS work on flow transition in 2010
-
108
Turbulence Modeling Limit of Eddy Viscosity Model -We cannot use
eddy viscosity assumption for flow separation
(There is no direct relation between Reynolds stress and
averaged strain
and eddy viscosity model has no scientific foundation )
Figure 4: 2' /u U in supersonic flow passing MVG
2' ' /u v UFIG. 5: Comparison of profiles of Stremwise velocity
U and at x/h = 22.8
At x/h=22.8 and y/h=2.5, both and are negative
x
w
z
uwu T ''
cannot stand unless
0T
which is impossible
''wu
z
u
-
Velocity Distribution in a transitional boundary layer
(turbulent boundary layer
Is similar) largest velocity and Reynolds stress are below the
displacement thickness
How to model ? Eddy Viscosity Model No Scientific Foundation
-
Conceptual Mistakes in Fundamental Fluid Dynamics
-
Conceptual Mistakes in Fundamental Fluid Dynamics
1. Considering multiple vortex rings are auto-generated 2.
Considering vortex was first attached on the wall and then detached
from the wall:
Vortex Line 3. Vortex breaks down and then reconnects:
0170M=0.5Vortex Vortex Line 4. Considering turbulence is generated
by unstable modes linear growth, interaction,
resonance, and breakdown either by absolute instability or
convective instability
BreakdownBuildup 5. Consider turbulent flow is a random motion:
Lander Bifurcation of Dynamics System Dynamics System N-S
N-SBifurcation
-
Conceptual Mistakes in Fundamental Fluid Dynamics
1. Considering small vortices are generated by large vortex
breakdown: RichardsonKolmokorovDNS Lambda2 Q 2. Turbulence is
velocity and pressure fluctuation: Fluctuation Euler 3.
Misunderstanding the vortex package structure and package motion
as
bursting and intermittency; 4. Not realizing the vortex ring has
a very fast rotating core (e.g. around
10,000 circles/second) with large gradient in velocity and
pressure. Of course, these misunderstandings are hard to be avoided
as our pioneering
scientists living in the 19th and early 20th centuries had
neither computers nor
high resolution experimental instruments. They mainly gave
hypotheses and
assumptions which must be re-examined.
?
-
My Understanding on Flow Transition
My understanding is that we do not need linear unstable
modes
but vorticity rollup which can be triggered by any perturbation,
then stretch,
shear layer Instability, shear transfers to rotation, large
vortex formation,
multilevel small vortices generation, chaos, and turbulence.
The nature of flow transition is that fluids cannot tolerate
strong shear and
shear must transfer to rotation (stable and with minimum energy
dissipation)
Flow transition is not a process of vortex breakdown but vortex
buildup
Flow transition is a process of vorticity redistribution from
near wall region
to the whole boundary layer
Flow transition is a process of transformation of irrotational
vorticity to rotational
vorticity while the shear is gradually reduced but rotation is
strengthened.
Vorticiy has rotational part and irrotational part.
-
Classical Theory VS My Theory on LBLT (In summary)
Receptivity Linear
Instability
Non-Linear
Instability
Vortex
breakdown
Turbulent
Flow
Large coherent
structure
Small Length
scale generation
Loss of symmetry
& flow chaos
The classical transition theory has an apparent logical problem:
vortex breaks down
to turbulence which is unstructured, why the turbulence
community still think and
study turbulence coherent structure (CS) and why the
transitional flow and turbulent
flow have similar structure?
Liu believes that the transition and fully developed turbulence
have same
mechanism. There is no vortex breakdown and shear layer
instability is the mother of turbulence. Turbulence is not
generated by vortex breakdown but vortex buildup
By using high order DNS in LBLT, Lius group has revealed many
new mechanisms, some of which are directly against the classical
theory
Classical Flow Transition Theory
My New Flow Transition Theory
Vorticity
Rollup Perturbation
-
Nature of Turbulence Generation 1.Fluids cannot tolerate high
shear and shear must transfer to rotation
and for a very fast rotation core (Dr. Cai will give his
experimental observation)
2. Turbulence is not generated by vortex breakdown but vortex
buildup 3. Shear layer instability is the mother of turbulence 4.
Turbulence small scales are generated by multiple level shear
layers which
Are generated by multiple level sweeps, ejections, negative and
positive spikes.
Nature of the Flow Transition 1.Vorticity redistribution from
near wall to whole boundary layer
2.Vorticity rollup
3.Irrotational vorticity transfer to rotational vorticity
4.Laminar flow dominated by shear (irrotational vorticity) is a
unstable state
5.Turbulent flow dominated by rotational vorticity is a stable
state (without
shear and then dissipation
1.k
-
Conceptual Mistakes in Fundamental Fluid Dynamics
1.Vortex is vortex tube? 2.Vorticity means rotation?
3.Vortex has large vorticity?
4.Vorticity line is vortex line?
5.Lambda vortex self-deforms to hairpin vortex?
All Wrong!
-
Conceptual Mistakes in Fundamental Fluid Dynamics
1. Considering multiple vortex rings are auto-generated
2. Considering vortex was first attached on the wall
and then detached from the wall:
3. Vortex breaks down and then reconnects
4. Considering turbulence is generated by unstable
modes linear growth, interaction, resonance, and
breakdown either by absolute instability or
convective instability
5. Consider turbulent flow is a random motion
All Wrong!
-
Conceptual Mistakes in Fundamental Fluid Dynamics
1. Considering small vortices are generated by large vortex
breakdown
2. Turbulence means velocity and pressure fluctuation:
3. Misunderstanding the vortex package structure and package
motion as
bursting and intermittency 4. Not realizing the vortex ring has
a very fast rotating core (e.g. around
10,000 circles/second) with large gradient in velocity and
pressure.
Of course, these misunderstandings are hard to be avoided as our
pioneering
scientists living in the 19th and early 20th centuries had
neither computers nor
high resolution experimental instruments. They mainly gave
hypotheses and
assumptions which must be re-examined.
-
Critical questions and my answers 1. Turbulent flow is random
and only has statistic value meaningful
No, turbulent flow cannot be random should turbulent flow follow
conservation of mass, momentum and energy? Turbulence has coherent
structure
2. Turbulence is generated by large vortex breakdown No, vortex
cannot break down and turbulence cannot be generated by vortex
breakdown but shear layer instability
3. Large eddies give energy to smaller eddies through vortex
breakdown No, through the sweeps not vortex breakdown
4. Turbulence consists of Richardson eddy cascade
No, Richardrson eddy cascade is never confirmed.
5. Turbulence is generated by unstable linear modes through
absolute instability or
Convective instability
No, the linear modes are always small and cannot develop vortex.
The role of all
Modes is to trigger vorticity rollup from wall and generate
inflection points.
6. The nature of flow transition is that shear is unstable,
rotation is stable, the fluids
cannot tolerate shear and shear layer must transfer to rotation,
or laminar flow must
transfer to turbulent flow.
7. There is no such a process that Lambda vortex self deforms to
hairpin vortex. Vortex
Ring is not part of Lambda vortex. Lambda root and vortex ring
are generated separately
By different mechanism.
-
My Comments on Flow Transition
My understanding is that we do not need linear unstable
modes
but vorticity rollup which can be triggered by any perturbation,
then stretch,
shear layer Instability, shear transfers to rotation, large
vortex formation,
multilevel small vortices generation, chaos, and turbulence.
The nature of flow transition is that fluids cannot tolerate
strong shear and
shear must transfer to rotation (stable and with minimum energy
dissipation)
Flow transition is not a process of vortex breakdown but vortex
buildup
Flow transition is a process of vorticity redistribution from
near wall region
to the whole boundary layer
Flow transition is a process of transformation of irrotational
vorticity to rotational
vorticity while the shear is gradually reduced but rotation is
strengthened.
Vorticiy has rotational part and irrotational part.
-
Classical Theory VS Our Theory on LBLT (In summary)
Receptivity Linear
Instability
Non-Linear
Instability
Vortex
breakdown
Turbulent
Flow
Large coherent
structure
Small Length
scale generation
Loss of symmetry
& flow chaos
There is no vortex breakdown and shear layer instability is the
mother of turbulence. Turbulence is not generated by vortex
breakdown but vortex buildup
Classical Flow Transition Theory
New Flow Transition Theory
Vorticity
Rollup Perturbation
-
Nature of Turbulence Generation 1.Fluids cannot tolerate high
shear and shear must transfer to rotation
and for a very fast rotation core (Dr. Cai will give his
experimental observation)
2. Turbulence is not generated by vortex breakdown but vortex
buildup 3. Shear layer instability is the mother of turbulence 4.
Turbulence small scales are generated by multiple level shear
layers which
Are generated by multiple level sweeps, ejections, negative and
positive spikes.
Nature of the Flow Transition 1.Vorticity redistribution from
near wall to whole boundary layer
2.Vorticity rollup
3.Irrotational vorticity transfer to rotational vorticity
4.Laminar flow dominated by shear (irrotational vorticity) is a
unstable state
5.Turbulent flow dominated by rotational vorticity is a stable
state (without
shear and then dissipation
-
123
Acknowledgments
This work was originally supported by AFOSR grant
FA9550-08-1-0201 supervised by Dr. John Schmisseur
and then the Department of Mathematics at University
of Texas at Arlington. The authors are grateful to Texas
Advanced Computing Center (TACC) for providing
computation hours. This work is accomplished by using
Code DNSUTA which was Developed by Drs. H. Shan,
L. Jiang and C. Liu at University of Texas at Arlington.
-
Thank You