AND CHARACTERISTICS OF TRANSITION TO TURBULENCE IN … · MTFC RESEARCH GROUP Future work – DMD...
Transcript of AND CHARACTERISTICS OF TRANSITION TO TURBULENCE IN … · MTFC RESEARCH GROUP Future work – DMD...
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
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• 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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• 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 3
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• 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 4
• 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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Equations MTFC RESEARCH GROUP
APS-DFD 2012 - San Diego, 18-20 November 2012 - V. Terrapon, Y. Dubief & J. Soria 5
Navier-Stokes for dilute polymer solutions
Polymer stress – FENE-P model
Polymer conformation tensor
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Equations MTFC RESEARCH GROUP
APS-DFD 2012 - San Diego, 18-20 November 2012 - V. Terrapon, Y. Dubief & J. Soria 6
Navier-Stokes for dilute polymer solutions
Polymer stress – FENE-P model
Polymer conformation tensor
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Simulated by-pass transition MTFC RESEARCH GROUP
APS-DFD 2012 - San Diego, 18-20 November 2012 - V. Terrapon, Y. Dubief & J. Soria 7
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
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Transition is promoted by viscoelasticity MTFC RESEARCH GROUP
APS-DFD 2012 - San Diego, 18-20 November 2012 - V. Terrapon, Y. Dubief & J. Soria 8
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
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2 states of the evolution considered MTFC RESEARCH GROUP
APS-DFD 2012 - San Diego, 18-20 November 2012 - V. Terrapon, Y. Dubief & J. Soria 9
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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Spatial statistics MTFC RESEARCH GROUP
APS-DFD 2012 - San Diego, 18-20 November 2012 - V. Terrapon, Y. Dubief & J. Soria 10
Mean velocity profile
z
U
-1 -0.5 0 0.5 10
0.5
1
1.5
Before
After
U
y
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z
Cii/L
2
-1 -0.5 0 0.5 10
0.25
0.5
0.75
1
Spatial statistics MTFC RESEARCH GROUP
APS-DFD 2012 - San Diego, 18-20 November 2012 - V. Terrapon, Y. Dubief & J. Soria 11
C ii /
L2
Mean polymer extension
Before
After
y
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Excitation of instabilities MTFC RESEARCH GROUP
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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?
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Poisson equation for pressure MTFC RESEARCH GROUP
APS-DFD 2012 - San Diego, 18-20 November 2012 - V. Terrapon, Y. Dubief & J. Soria 13
Extended Poisson equation
f(x)
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Poisson equation for pressure MTFC RESEARCH GROUP
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Extended Poisson equation
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)
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Poisson equation for pressure MTFC RESEARCH GROUP
APS-DFD 2012 - San Diego, 18-20 November 2012 - V. Terrapon, Y. Dubief & J. Soria 15
Extended Poisson equation
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
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Influence function MTFC RESEARCH GROUP
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Source of contribution to pressure at point P from relative “unorganized” free-stream turbulence in channel center
Before nonlinear breakdown of instabilities
F(ξ,x)
Point P
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Influence function MTFC RESEARCH GROUP
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Source of contribution to pressure at point P from relative “unorganized” free-stream turbulence in channel center
Before nonlinear breakdown of instabilities
F(ξ,x)
Source of contribution to pressure at point P from elastically induced more “organized” structures in near-wall region
After nonlinear breakdown of instabilities
F(ξ,x)
Point P
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Plane-averaged pressure fluctuations MTFC RESEARCH GROUP
APS-DFD 2012 - San Diego, 18-20 November 2012 - V. Terrapon, Y. Dubief & J. Soria 18
p2 (!) = h(y;!)dy!H
H
"
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Plane-averaged pressure fluctuations MTFC RESEARCH GROUP
APS-DFD 2012 - San Diego, 18-20 November 2012 - V. Terrapon, Y. Dubief & J. Soria 19
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
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Plane-averaged pressure fluctuations MTFC RESEARCH GROUP
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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
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Conclusions MTFC RESEARCH GROUP
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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
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Future work – DMD analysis
APS-DFD 2012 - San Diego, 18-20 November 2012 - V. Terrapon, Y. Dubief & J. Soria 22
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)
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Future work – DMD analysis
APS-DFD 2012 - San Diego, 18-20 November 2012 - V. Terrapon, Y. Dubief & J. Soria 23
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)
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Future work – DMD analysis
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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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Vortices and extensional flow MTFC RESEARCH GROUP
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Before nonlinear breakdown of instabilities
Weak homogeneous isotropic turbulence
Qa = 0.02 Qa = -0.02
After nonlinear breakdown of instabilities
Few hairpin-like vortices followed by train of alternating “rotational” and “straining” flow at very small scales
Qa = 0.2 Qa = -0.2