Flow Control and Turbulence Modelingwpi/themedata/Arkady_WS/... · 2011. 2. 17. · Flow Control with Additives ¾additives (especially long-chain polymers) are used in practical

03. Februar 2010 | B.Frohnapfel | 1

Bettina FrohnapfelCenter of Smart Interfaces

TU Darmstadt

Workshop"Models versus physical laws/first principles, or why models work?"

Wolfgang Pauli Institute, Vienna, Austria, February 2-5, 2011

Flow Controland

Turbulence Modeling


Goals in Turbulence Research

“understanding”

modelingprediction control

Turbulence

?S.B. Pope (PoF 2011, based on APS Otto Laporte Lecture 2009):The objective of developing theories and models is of particular importance as the methodologies developed often can be used to achieve other objectives such as control of turbulent flows.


Goals of Flow Control

transition reattachment

separation

drag lift/circulation

transition in free-shear layermay lead to reattachment

skin-frictiondrag

higheraftertransition

enhanceslift

induced drag

lift-to-drag ratio

laminar boundary layer

succeptible to separation

may lead to transition

in free shear layer

turbu

lent b

ound

arylay

er

resist

ent to

sepa

ration

leads to

loss of liftreduce

s form

drag

increa

ses

form

drag

Gad-el-Hak, 2000


Skin Friction Reduction

Wall

w dxUd

⎟⎟⎠

⎞⎜⎜⎝

⎛=

2

1μτ221 U

c wfρ

τ=Friction coefficient

Drag reduction in turbulent flows

Postpone laminar to turbulent transition to higher Reynolds numbers

old ,

new ,1w

wDRττ

−=


Drag in a Flow Field

Skin friction drag constitutes• 40 - 50% of the total drag on

airplanes

• 50 - 90% of the total drag on (under)water vehicles

• up to 100% of the total drag in pipelines

Fantasy of Flow, 1993

Possible savings• 20% drag reduction on airplanes

1 Billion Dollar/Year (Gad el Hak, 2000)

• 10% drag reduction on surface ships5 Billion Dollar/Year (Gollup, 2006)

• 7 instead of 10 pumpstations in Transalaska Pipeline (www.alyeska-pipe.com)


Flow Control Methods

Passive

Active(predetermined)

Reactive(closed loop)

high friction low friction

Attenuation of QSV

AdditivesMorphologyPhysical Chemistry

Actuators:Wall movementWall fluxesBody Forces

Actuators & Sensors:Wall movementWall fluxesBody Forces


Flow Control with Additives

additives (especially long-chain polymers) are used in practical applications

research: experimental & DNS

in DNS: model of polymer-flow interaction

some remaining discrepancies between experiment and DNS and different “opinions” in respect to the underlying physical mechanism

additives cannot be used in all situations, but the engineering dream would be to reproduce this DR effect by other means!

RANS prediction?www.wikipedia.de

current DR world record: 96.5% at Re=200.000, flow with polymeric and fibrous additives in pipe with Ø 2.4cm (Lee et al. 1974)


Flow Control with Riblets

Ribletsexperiments: broad parameter studyanalytical work for viscous regimeDNS

high Re-number testing on airplanes (1-2% fuel saving),application on yacht for America’s cup

front view of riblet surface

drag

diff

eren

ce [%

]

s+=uτs/ν

DLR:technical optimum

NASA-Riblets

DLR-Riblets

ribletsBechert et al. (2000)

goal: increase drag reducing potential to reach break even point for applications


sinusoidal riblets / 3D riblets

Using LES for flow control- wavy riblets

Peet & Sagaut (2009)

LES ResultsDRmax ≈ 14%

DNS & Experiments (Berlin group, 2010): no positive effects of sinusoidal shape

Kramer et al. (2010)


(Re-)Active Control

Net energy budgetPumping power: Power saving: Control input:

DefinitionsNet energy saving

energy gainEnet = P − P '( )− Pin

G =EnetPin

Control input

Reduced pumping power

Reactive control: G = 100 ~ 300 Active control: G ~ 1.7

P'P

inP'PP −

Net energy savings are difficult to realize!


Challenges for Reactive Control

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

very high pressure gas pipeline

ship/high pressure gas pipeline

gas pipeline

petroleum pipeline

automobile

bullet train/maglev

aircraft

liqui

dga

s

time

[ms]

length [mm]

typical length scaleof near-wall vortices

typical time scaleof near-wall vortices

10µm – 1mm

10µs – 10ms

MEMS

real time control

Kasagi et al., 2009


Present Challenges

active and reactive control is mostly done in DNS (low Reynolds number)very few experiments (also at low Re) – proof of principle

arrayed hot-film sensor and wall deformation actuatorsGA optimization, 10hour optimization, about 6% DR

Yoshino et al., 2008reactiveAuteria et al., 2010

travelling wave in pipeDRmax ≈30%, Gopt≈1.5 Greal≈2.4*10-5 (huge net losses)

predetermined


polymer drag reduction

streamwise travelling waves of spanwise wall velocity, DR decreases weakly with Reynolds number (up to Reb=10000), similar for spanwise wall oscillation; further tests with LES did not produce comparable results to DNS so far

Reynolds Number Dependency

Tilli et al. 2003


Reynolds Number Dependency

ideal damping of turbulence near the wall, weak Reynolds number dependence

If it were possible to capture viscous drag reduction with turbulence models important insight in respect to the Re-number dependency could be gained…

Iwamoto et al., 2005

(damping of large scale structures is less effective)


Turbulent Channel Flow

fully developed,two dimensional

energy balance

VPP &Δ=

Power requirement

Flow

momentum balance(RANS) Fukagata et al., 2002


0.001

0.01

0.1

102 103 104 105

total dissipation

Skin Friction and Energy Dissipation Rate

0.001

0.01

0.1

102 103 104 105

turbulent dissipationdirect dissipationtotal dissipation


Total Energy Dissipation Rate

max possible saving?


Turbulent Dissipation

turbulent dissipation

turbulent dissipation rate

drag reduction

0.001

0.01

0.1

102 103 104 105


two componentturbulence

axisymmetric turbulence

isotropicturbulence

Lumley 1978

IIa= aijaji

IIIa= ajkakjaij

ijji

ij quu

a δ31

2 −=

IIa

IIIa

one componentturbulence

Anisotropy-Invariant Map

two componentisotropic turbulence

0.4

0.1-0.1 0.3


Turbulent Dissipation at the Wall

εwall


series expansion for uj around the wallMonin and Yaglom (1987)

local axisymmetry (around x1-axis)George and Hussein (1991)

...222211 ++= xaxau

...2222 += xbu

...222213 ++= xcxcu02 →xfor

2

3

1

2

2

1⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

=⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

n

n

n

n

xu

xu

2

3

3

2

2

2⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

=⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

n

n

n

n

xu

xu

2

2

3

2

3

2⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

=⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

n

n

n

n

xu

xu

( ) 02121 →+≈ caυ

The Limiting State at the Wall

all coefficientshave to vanish

02=

⎟⎟⎠

⎞⎜⎜⎝

⎛∂

∂

∂

∂=

xi

j

i

jw x

uxu

νε


Numerical Experiments

suppression of the spanwise velocity fluctuations

DR

6%

19%

30%

42%


0.00

0.04

0.08

0.16

0 50 1500.0

0.1

0.2

0.3

0.4

0.5

0.7

0.00 0.20

suggested drag reduction mechanism can be reproduced in DNSeffects within viscous sublayer – probably impossible with any RANS approach

„need to put a model near the wall“

uncontrolledcontrolled, yD+= 5

Numerical Experiments


DNS Data: Dimitropouloset al. (1998) R = 15% R = 44%

R = 0%

x2 0

x2 0x2 0

Polymer Drag Reduction

near wall fluctuations:statistically axisymmetric &invariant under rotation about theaxis aligned with the mean flow


Quantitative Relation

FIK Identity: Fukagata et al.,2002


Shear Stress Contribution: w‘-damping

0 50 100 1500

1

2

3

4

5

6

7

8

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0 50 100 150x₪2 x₪2


0

2

4

6

8

10

0 50 100 1500.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 50 100 150

uncontrolled channel flow

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0 50 100 150

Shear Stress Contribution: u‘-enhancement


Spanwise Wall Oscillation

spanwise oscillationDR=25%uncontrolled channel flow

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0 50 100 1500.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0 50 100 150


0.0

0.5

1.0

1.5

2.0

0 50 100 1500

5

10

15

20

25

30

35

0 50 100 150

spanwise oscillation, DR=25%uncontrolled channel flow

source of drag reduction: reduced eigenvalue difference physical meaning?

Spanwise Wall Oscillation


statistical

fc Hagen – Poiseuille LawLaminar flowPrandtl – Karman LawTurbulent flow

Transition

(Re)crit

deterministic

Rλ2

ε∼

Learn Something about Transition?

BUuD

2~

τ

εε =

2Re λR∝

Re(Rλ)crit


Cantwell, Coles, Dimotakis 1978

Nishi 2009

Turbulent Spots


kk

ji

k

j

k

i

ji

ij

k

jki

k

ikj

ji

xxuu

xu

xu

xpu

xpu

xU

uuxUuu

DtuuD

∂∂

∂+

∂

∂

∂∂

−⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂∂

+∂∂

−∂

∂−

∂∂

−=''2'''

''

'''''''

21 υυρ

ii Uu


kk

jiijhijhijijssssijij

ji

xxuu

aAPPFPaPDt

uuD∂∂

∂+−−⎟

⎠⎞

⎜⎝⎛ −++≅

''2''

21

322

31 υδεεδ

kkhk xx

kPDtDk

∂∂∂

+−≅2

21νε

( )''21

ssuuk =

Transport equations for the evolution of statistically axisymmetric disturbances:

kk

hhkihh

xxkkuuA

DtD

∂∂∂

+−−≅ευεψεε

22''

212

( )λψ RIIIIIfA aa ,, , =( )aa IIIIIfF , =

Energy equation for the disturbances:

LDA data of Becker et al. (1999)u12/(u12)∞

Modeled Equations


( )kk

hhh

xxkA

DtD

∂∂∂

+−≅ενεψε

22

21 2 hkP ε≅

Dissipation equation for the disturbances:

with

( )λψ RIIIIIfA aa ,, , =transition criterion: 0 -2 ≥ψA where

Rλ = (Rλ)crit

Rλ (Rλ)crit

Rλ (Rλ)crit

Dissipation Equation


0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.160

200

400

600

800

1000

1200

1400

1600

1800

2000

II

unstable

stab

le

transform transition criterion in terms of (Rλ)T = f(IIa)

(Rλ)T

(IIa)∞

(Rλ)T=13.55 (IIa)∞≈ 0.15

Transition Criterion


Tu [%]

(Rex)T

(IIIa)∞ < 0 (IIIa)∞ > 0

x106

Spangler and Wells, LTV (1968)Schubauer and Skramstadt, NBS (1943) ITAM Novosibirsk

LSTM Erlangen

HFI Berlin

NASA Langley

“theory”, (IIa)∞= 0

0

1

2

3

4

5

6

7

0 0.05 0.10 0.15 0.20

Overview: Transition Experiments


Enhanced communication between turbulence modeling/ turbulence theory and flow control community might provide valuable insight

Understanding/ models that were obtained for prediction purposes can provide insight into flow control options/ limitations

Can modifications of skin friction drag be captured with RANS or LES?

- Reynolds number scaling- application to “real” problems

Conclusions/ Open Questions

Goals in Turbulence ResearchGoals of Flow ControlSkin Friction ReductionDrag in a Flow FieldFlow Control MethodsFlow Control with AdditivesFlow Control with RibletsUsing LES for flow control�- wavy ribletsChallenges for Reactive ControlPresent ChallengesReynolds Number DependencyTurbulent Channel FlowAnisotropy-Invariant MapTurbulent Dissipation at the WallPolymer Drag ReductionQuantitative RelationShear Stress Contribution: w‘-dampingShear Stress Contribution: �u‘-enhancementSpanwise Wall OscillationSpanwise Wall Oscillation

Documents

Flow Control and Turbulence Modelingwpi/themedata/Arkady_WS/... · 2011. 2. 17. · Flow Control with Additives ¾additives (especially long-chain polymers) are used in practical