1. Evolution of a turbulent patch in dilute polymer
solutions
April 27, 2015
Mark Baevsky and Alex Liberzon
www.eng.tau.ac.il/turbulencelab
Turbulence Structure Laboratory
School of Mechanical Engineering
Tel Aviv University
2. 1
Contents
Turbulent flows of dilute polymer solutions
Experimental arrangement
Results
Conclusions
Note: All DNS simulations were performed by our partners, G. Cocconi and B. Frohnapfel from
Karlsruhe Institute of Technology, Germany: and E. De Angelis from Università di Bologna, Italy
3. 2
Polymer chain in a turbulent flow
< R2 >0 = 253 nanometers
Turbulence
=⇒
lmax = 65 microns
Note: Chain dimensions estimations are for Mw = 8000000 -
poly(ethylene oxide) used in our experiments.
4. 3
Drag reduction
Drag reduction is the most widely known effect of the dilute (∼10
wppm) polymer solutions.
Suppression of cross-stream fluctuations.
Modification of the boundary layer profile.
Reduction of turbulent cross-stream diffusion of the flow
momentum as a result.
Turbulent boundary layer visualized using cross-stream fronts of hydrogen
bubbles. From Y. Iritani, N. Kasagi and M. Hirata 1980.
5. 4
Reduced entrainment rate
Entrainment characteristics across turbulent/non-turbulent
interface (TNTI) are also of a great interest.
High velocity gradients at the interface =⇒ high polymers activity.
Result: reduced entrainment rate per unit energy inside the jet.
Turbulent mixing in jets of water(left) and ’Polyox’(right). From [Gadd, 1965].
6. 5
Particle image velocimetry (PIV)
Typical experimental arrangement for PIV in a wind tunnel. From
[Raffel et al., 2007]
9. 8
Time evolution of vorticity ω(r, θ, t)
Vorticity magnitude maps for (from left to right) water,5ppm,10ppm at
8.4 Hz agitation frequency.
10. 9
Average kinetic energy profiles q(r)
Kinetic energy per unit mass q = (u2
+v2
)
2
10
2
10
0
10
1
10
2
r [mm]
q[mm/sec]2 water, t=1s
t=3s
t=10s
5 wppm, t=1s
t=3s
t=10s
10 wppm, t=1s
t=3s
t=10s
Spatially averaged profiles of kinetic energy q(r) θ at t=1,3 and 10 seconds, versus radial
coordinate r for 10.5 Hz agitation frequency. All profiles start from the edge of the agitation device ,
r = 24 mm.
11. 10
Average enstrophy profiles ω(r)
10
2
10
−3
10
−2
10
−1
10
0
r [mm]
ω2
s−2
water, t=1s
t=3s
t=10s
5 wppm, t=1s
t=3s
t=10s
10 wppm, t=1s
t=3s
t=10s
Spatially averaged profiles of enstrophy ω2
θ at t=1,3 and 10 seconds, versus radial coordinate r
for 10.5 Hz agitation frequency. All profiles start from the edge of the agitation device , r = 24 mm.
12. 11
Patch and interface identification
ξ(t) =
(dreq/dt)
2 · ECV /(ρ · A)
(1)
x[mm]
y[mm]
20 40 60 80 100120
20
40
60
80
100
120
140
x[mm]
20 40 60 80 100120
20
40
60
80
100
120
140
x[mm]
20 40 60 80 100120
20
40
60
80
100
120
140
ω2
(s−2
)
0
5
10
15
20
An example of the patch identification snapshots in water at agitation frequency of 10.5 Hz at t=1,3
and 10 seconds. The color-map is enstrophy, white dots fill the patch zone and the red ones
represent TNTI.
13. 12
Evolution of the patch kinetic energy
0 5 10 15 20 25 30
−2
−1
0
1
2
3
4
5
6
7
8
x 10
−5
t [sec]
ECV−Et=0
CV[Joule/m]
water 6.9[Hz]
water 8.4[Hz]
water 10.5[Hz]
5ppm 6.9[Hz]
5ppm 8.4[Hz]
5ppm 10.5[Hz]
10ppm 6.9[Hz]
10ppm 8.4[Hz]
10ppm 10.5[Hz]
(Left) Ensemble average of kinetic energy per unit length inside the control volume calculated from
PIV velocity fields.(Right) DNS turbulent kinetic energy normalized by the forcing frequency f and by
the forcing mesh size M.
14. 13
Entrainment rate, ξ
ξ(t) =
(dreq/dt)
2 · ECV /(ρ · A)
(2)
0 2 4 6 8 10
0.4
0.5
0.6
0.7
0.8
0.9
1
Cpolymer[wppm]
<ξ>
6 7 8 9 10 11
0.4
0.5
0.6
0.7
0.8
0.9
1
f[hz]
<ξ>
water 6.9[Hz]
water 8.4[Hz]
water 10.5[Hz]
5ppm 6.9[Hz]
5ppm 8.4[Hz]
5ppm 10.5[Hz]
10ppm 6.9[Hz]
10ppm 8.4[Hz]
10ppm 10.5[Hz]
(Left) Estimated entrainment coefficients versus the polymer concentration for different agitation
frequencies. (Right) Estimated entrainment coefficients versus agitation frequency for different
polymer concentrations. Calculated using equation 2.
15. 14
3D-PTV patch average TNTI positions r(t)
0 5 10 15 20 25 30
0
10
20
30
40
50
60
70
80
90
t(sec)
r(mm)
5ppm ~10 Hz
Water ~10 Hz
Average TNTI radial position r versus time t, from 3D-PTV experiments.
16. 15
Particle trajectories crossing TNTI
−5 0 5 10 15 20 25 30
−10
0
10
20
30
40
50
60
70
t(sec)
r(mm)
log(ω2
z)
−25
−20
−15
−10
−5
0
−5 0 5 10 15 20 25 30
−10
0
10
20
30
40
50
60
70
t(sec)
r(mm)
log(ω2
z)
−25
−20
−15
−10
−5
0
Particle trajectories which cross the TNTI (left) into the patch and (right) out of the patch, in
polymer solution.
17. 16
Particle trajectories crossing TNTI
0 5 10 15 20
20
30
40
50
60
70
80
90
t(sec)
r(mm)
log(ω2
z)−25
−20
−15
−10
−5
0
0 5 10 15 20
20
30
40
50
60
70
80
90
t(sec)
r(mm)
log(ω2
z)
−20
−18
−16
−14
−12
−10
−8
−6
−4
−2
Particle trajectories which cross the TNTI (left) into the patch and (right) out of the patch, in water.
18. 17
Conclusions and future work
Comparing polymer solutions to water benchmark case.
Smoother turbulent/non-turbulent interface ⇐⇒ Lower flow length
scales diversity.
Consistently lower entrainment rate coefficient ξ.
Higher kinetic energy density inside the patch.
Future work
3D-PTV to validate the 2D results and to provide a better insight.
Broader polymer concentrations range (0-10 wppm in current
experiments).
Higher Re numbers.
20. 19
References
[Gadd, 1965] Gadd, G. (1965).
Turbulence damping and drag reduction produced by certain additives in water.
Nature, 206, 463–467.
[Raffel et al., 2007] Raffel, M., Willert, C. E., Wereley, S. T., & Kompenhans, J. (2007).
Particle Image Velocimetry a practical guide.
Number 2007928306. Springer, 2 edition.
