Download presentation

Presentation is loading. Please wait.

Published byJessica Wiley Modified over 4 years ago

1
On bifurcation in counter-flows of viscoelastic fluid

2
Preliminary work Mackarov I. Numerical observation of transient phase of viscoelastic fluid counterflows // Rheol. Acta. 2012, Vol. 51, Issue 3, Pp. 279-287 DOI 10.1007/s00397-011-0601-y. Mackarov I. Dynamic features of viscoelastic fluid counter flows // Annual Transactions of the Nordic Rheology Society. 2011. Vol. 19. Pp. 71-79.

3
One-quadrant problem statement:

4
The process of the flow reversal, Re = 0.1, Wi = 4, mesh is 675 nodes, t=1.7 ÷2.5

6
G.N. Rocha and P.J. Oliveira. Inertial instability in Newtonian cross-slot flow – A comparison against the viscoelastic bifurcation. Flow Instabilities and Turbulence in Viscoelastic Fluids, Lorentz Center, July 19-23, 2010, Leiden, Netherlands R. J. Poole, M. A. Alves, and P. J. Oliveira. Purely Elastic Flow Asymmetries. Phys. Rev. Lett., 99, 164503, 2007.

7
Vicinity of the central point: symmetric case

8
Symmetry relative to x, y gives

9
Symmetry relative to x, y defines the most general asymptotic form of velocities: … and stresses:

10
Substituting this to momentum, continuity, and UCM state equations will give…

12
(21), Symmetry on x, y involves Therefore, for the rest of the coefficients in solution

13
Pressure: from momentum equation where

14
Comparison with symmetric numerical solution

15
Via finite-difference expressions of coefficients in velocities expansions, we get from the numeric solution: A -0.006 B 0.0032

16
STRESS: Σ x = -0.0573 α = 0.0286 β = 0.026 α σ xx = -0.0518 Via finite-difference determination of coefficients in velocities expansions get : Numerical stress in the central point :

17
Normal stress distribution in numeric one-quadrant solution (stabilized regime), Re=0.1, Wi=4, the mesh is 2600 nodes

18
PRESSURE: Via finite-difference values of coefficients in velocities expansions, we get : P x =0.0642 P y =-0.0641 - P x

19
Same for the pressure

20
Vicinity of the central point: asymmetric case

21
UCM model, Re = 0.01, Wi = 100, t = 3.55, mesh is 6400 nodes

22
Looking into nature of the flow reversalanalogy with simpler flows Looking into nature of the flow reversal : analogy with simpler flows Couette flow Couette flow Poiseuille flow Poiseuille flow

23
Whole domain solution

24
UCM model, Re = 0.1, Wi = 4, t=2.7, mesh has 2090 nodes

25
Pressure distribution in the flow with Re = 3 and Wi = 4 at t = 3.5, mesh is 1200 nodes, Δt = 5·10 -5

26
Conclusions

27
Both some features reported before and new details were observed in simulation of counter flows within cross-slots (acceleration phase). Among the new ones: the pressure and stresses singularities both at the stagnation point and at the walls corner, flow reversal with vortex-like structures. The flow reverse is shown to result from the wave nature of a viscoelastic fluid flow.

28
Tried lows of the pressure increase:

29
Flow picture (UCM model, Re = 0.05, Wi = 4, t=6.2), with exponential low of the pressure increase (α = 1) the mesh is 432 nodes

30
Convergence and quality of numerical procedure

31
Picture of vortices typical for typical for small Re. UCM model, Re = 0.1, Wi = 4, t=2.6, mesh is 1200 nodes

32
The same flow snapshot (UCM model, Re = 0.1, Wi = 4, t=2.6), obtained on a non-elastic mesh with 1200 nodes

33
Normal stress distribution in the flow with Re = 0.01 and Wi =100 at t = 3; UCM model, mesh is 2700 nodes, Δt= 5·10 -5

34
Sequence of normal stress abs. values at the stagnation point. Smaller markers correspond to time step 0.0001, bigger ones are for time step 0.00005

36
Normal stress distribution in the flow with Re = 0.1 and Wi =4 at t = 3; mesh is 450 nodes, Δt= 5·10 -5

37
Used lows of inlet pressure increase:

38
The process of the flow reversal, Re = 0.1, Wi = 4, mesh is 675 nodes, t=1.7 ÷2.5

39
Flow picture for Re = 0.1, Wi = 4, the mesh is 4800 nodes

42
Extremely high Weissenberg numbers

43
Flow picture for Re = 0.01, Wi = 100, the mesh is 4800 nodes

50
A flow snapshot from S. J. Haward et. al., The rheology of polymer solution elastic strands in extensional flow, Rheol Acta (2010) 49:781-788

Similar presentations

OK

About TIME STEP In solver option, we must define TIME STEP in flow solver.

About TIME STEP In solver option, we must define TIME STEP in flow solver.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google