AND CHARACTERISTICS OF TRANSITION TO TURBULENCE IN … · MTFC RESEARCH GROUP Future work – DMD analysis" APS-DFD 2012 - San Diego, 18-20 November 2012 - V. Terrapon, Y. Dubief

MTFC RESEARCH GROUP

MTFC RESEARCH GROUP

MECHANICS AND CHARACTERISTICS ��OF TRANSITION TO TURBULENCE ��IN ELASTO-INERTIAL TURBULENCE

Vincent E. Terrapon University of Liège, Belgium Yves Dubief University of Vermont, VT Julio Soria Monash University, Australia

King Abdulaziz University, Kingdom of Saudi Arabia Financial support Marie Curie FP7 CIG, Vermont Advanced Computing Center, National Institutes of Health, Australian Research Council, Center for Turbulence Research Summer Program

MTFC RESEARCH GROUP

MTFC RESEARCH GROUP

MTFC RESEARCH GROUP

•  Formation of sheets

•  Excitation of extensional sheet flow

•  Elliptical pressure redistribution of energy

•  Increase of extensional viscosity

Context and objectives MTFC RESEARCH GROUP

APS-DFD 2012 - San Diego, 18-20 November 2012 - V. Terrapon, Y. Dubief & J. Soria 2

Channel flow

Polymer extension

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MTFC RESEARCH GROUP







MTFC RESEARCH GROUP

MTFC RESEARCH GROUP







•  How do long-range interactions through pressure contribute to transition?

•  What locations in the flow contribute most to instability excitation?

•  What is the relative contribution of both terms in the Poisson equation?

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MTFC RESEARCH GROUP

Equations MTFC RESEARCH GROUP


Navier-Stokes for dilute polymer solutions

Polymer stress – FENE-P model

Polymer conformation tensor

MTFC RESEARCH GROUP

MTFC RESEARCH GROUP

Equations MTFC RESEARCH GROUP


Navier-Stokes for dilute polymer solutions

Polymer stress – FENE-P model

Polymer conformation tensor

MTFC RESEARCH GROUP

MTFC RESEARCH GROUP

Simulated by-pass transition MTFC RESEARCH GROUP


2H 3.3H

6.6H

x

z

y

Parameters

•  Wi = 400 •  L = 200 •  Re = Ub H / ν = 1000 •  β = 0.9

Periodic channel flow

1.  Plug flow with slip

2.  Injection of homogeneous isotropic turbulence in channel center

3.  No-slip at the wall

HIT

MTFC RESEARCH GROUP

MTFC RESEARCH GROUP

Transition is promoted by viscoelasticity MTFC RESEARCH GROUP


dP/d

x

t

1

2

3

4 x 103

0 500 1000

Evolution of wall friction

Newtonian

Viscoelastic

u’/Ub=0.006

u’/U

b=0.

025

u’/U

b=0.

020

u’/U

b=0.

015

•  Viscoelastic flow transitions with weaker perturbations

•  Same perturbation level would lead to laminar Newtonian flow

•  Viscoelastic flow transitions to MDR and stays at MDR

MTFC RESEARCH GROUP

MTFC RESEARCH GROUP

2 states of the evolution considered MTFC RESEARCH GROUP


dP/d

x

t

1

2

3

4 x 103

0 500 1000

Before nonlinear breakdown of instabilities

After nonlinear breakdown of instabilities

Evolution of wall friction u’

/Ub=

0.02

5

u’/U

b=0.

020

u’/U

b=0.

015

u’/Ub=0.006

Newtonian

Viscoelastic

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MTFC RESEARCH GROUP

Spatial statistics MTFC RESEARCH GROUP


Mean velocity profile

z

U

-1 -0.5 0 0.5 10

0.5

1

1.5

Before

After

U

y

MTFC RESEARCH GROUP

MTFC RESEARCH GROUP

z

Cii/L

2

-1 -0.5 0 0.5 10

0.25

0.5

0.75

1

Spatial statistics MTFC RESEARCH GROUP


C ii /

L2

Mean polymer extension

Before

After

y

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MTFC RESEARCH GROUP

Excitation of instabilities MTFC RESEARCH GROUP


Isotropic turbulence

Elastic instabilities

y+

log10 kx

Power spectrum of the elastic energy before nonlinear breakdown of instabilities

No diffusion yet

•  Instabilities in near-wall regions not caused by diffusion of turbulence from channel center

•  What triggers the instability?

MTFC RESEARCH GROUP

MTFC RESEARCH GROUP

Poisson equation for pressure MTFC RESEARCH GROUP


Extended Poisson equation

f(x)

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MTFC RESEARCH GROUP




Pressure kernel – Green function G

“Influence” function F(x, ξ) represents the contribution of point x to the pressure at point ξ

+ B.C.

f(x)

MTFC RESEARCH GROUP

MTFC RESEARCH GROUP




Pressure kernel – Green function G

“Influence” function F(x, ξ) represents the contribution of point x to the pressure at point ξ

+ B.C.

f(x)

Green function G(0, -0.9H, 0; x, y, z)

x

z

y

MTFC RESEARCH GROUP

MTFC RESEARCH GROUP

Influence function MTFC RESEARCH GROUP


Source of contribution to pressure at point P from relative “unorganized” free-stream turbulence in channel center


F(ξ,x)

Point P

MTFC RESEARCH GROUP

MTFC RESEARCH GROUP

Influence function MTFC RESEARCH GROUP


Source of contribution to pressure at point P from relative “unorganized” free-stream turbulence in channel center


F(ξ,x)

Source of contribution to pressure at point P from elastically induced more “organized” structures in near-wall region


F(ξ,x)

Point P

MTFC RESEARCH GROUP

MTFC RESEARCH GROUP

Plane-averaged pressure fluctuations MTFC RESEARCH GROUP


p2 (!) = h(y;!)dy!H

H

"

MTFC RESEARCH GROUP

MTFC RESEARCH GROUP



p2 (!) = h(y;!)dy!H

H

"

z

h(z)

-1 -0.5 0 0.5 1-1

-0.5

0

0.5

1 10-7Before nonlinear breakdown

h(y;η)

y

Total

2Qa

MTFC RESEARCH GROUP

MTFC RESEARCH GROUP



p2 (!) = h(y;!)dy!H

H

"

z

h(z)

-1 -0.5 0 0.5 1-1

-0.5

0

0.5

1 10-7Before nonlinear breakdown

h(y;η)

y

Total

2Qa

z

h(z)

-0.5 0 0.5-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5 10-4After nonlinear breakdown

h(y;η)

Total

2Qa

z

h(z)

-1 -0.5 0 0.5 1-1

-0.5

0

0.5

1 10-7

-2.5"

y

MTFC RESEARCH GROUP

MTFC RESEARCH GROUP

Conclusions MTFC RESEARCH GROUP


Current understanding of viscoelastic transition

• Long-range excitation of elastic instabilities through pressure

• Feeding of energy to elastic instabilities from mean flow

• Elastic instabilities then self-sustained

• Polymeric contribution in Poisson equation dominates kinematic contribution

MTFC RESEARCH GROUP

MTFC RESEARCH GROUP

Future work – DMD analysis


Re = 1000 Re = 3000

fr fr

A

100

101

-5 5 0 -5 5 0

Mode amplitude as a function of frequency from DMD analysis Q invariant (streamwise – wall-normal plane)

•  Shape change with increasing Re •  At larger Re, two apparent contributions

•  Hypothesis: elastic and inertial (to be verified)

MTFC RESEARCH GROUP

MTFC RESEARCH GROUP



Re = 1000 Re = 3000

fr fr

A

100

101

-5 5 0 -5 5 0

Mode amplitude as a function of frequency from DMD analysis Q invariant (streamwise – wall-normal plane)

Inertial ?

Elastic ?

•  Shape change with increasing Re •  At larger Re, two apparent contributions

•  Hypothesis: elastic and inertial (to be verified)

MTFC RESEARCH GROUP

MTFC RESEARCH GROUP



Most amplified mode from DMD analysis Q invariant (streamwise – wall-normal plane) at Re=1000

•  Mostly two-dimensional structures

•  Located in near-wall region

•  Alternating pressure minima and maxima

•  “Discontinuity” close to wall corresponding to location of extremum of mean polymer extension (critical layer?)

0.15-0.2

y/h

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MTFC RESEARCH GROUP

Vortices and extensional flow MTFC RESEARCH GROUP



Weak homogeneous isotropic turbulence

Qa = 0.02 Qa = -0.02


Few hairpin-like vortices followed by train of alternating “rotational” and “straining” flow at very small scales

Qa = 0.2 Qa = -0.2

Documents

AND CHARACTERISTICS OF TRANSITION TO TURBULENCE IN … · MTFC RESEARCH GROUP Future work – DMD analysis" APS-DFD 2012 - San Diego, 18-20 November 2012 - V. Terrapon, Y. Dubief