lecture 1 tgs2015a new theory turbulence cliu june 2015n

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

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

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)

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

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:

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)

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


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)

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

Bypass

Morkovin (1984)

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)

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

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

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)

Vortices generated by water jet (Cais experimental observation with highest resolution

of 1 , personal contact) m

How Fast is the Ring Rotation?

What Is Turbulence?

My understanding:

Turbulent flow is a rotation dominant,

chaotic flow with different size of

vortices.

By P. Roache, 1968

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.


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)

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

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 .


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


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

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.

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.

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.

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)

Streaks Lift-Up and Form Hairpin

Hairpins Inclined at 45 deg. (Principal Axis)

First Evidence of Theodorsens Hairpins

Re = 1700

Short Review by Moin

Streaks Lift-Up and Form Hairpin

For Increasing Re, Hairpin Elongates and Thins

Streamwise Vortex Forms the Hairpin Legs


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


Packets of Hairpins Kim and Adrian (1982)

VLSM Arise From Spatial Coherence of Hairpin Packets

Hairpin Packets Align & Form Long Low-Speed Streaks (>2)


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


Velocity and Stress

of Laminar and Turbulent

Flow (Adrian 2007)

Turbulence increases

velocity near the bottom

but decreases in the middle.

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

Velocity Distribution

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

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

38

XIAOHUA WU and PARVIZ MOINProfessor, Director Center for Turbulence Research, Stanford University

39

Dan Henningson, Professor, Director,

Swedish e-Science Research Centre, KTH Mechanics

Transition in Boundary Layer Flow over Flat Plate

40

41

Transition in Boundary Layer Flow over Flat Plate Contd

42

Turbulent Boundary Layer

43

Turbulent Boundary Layer Contd

44

Turbulent Boundary Layer Contd (Jets)

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

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!

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

Let US Take a Break!

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

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?

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


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


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


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!


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!


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

lecture 1 tgs2015a new theory turbulence cliu june 2015n

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