Three cases were studied :

1. Phan Tien - Tanner model : Deborah number = 1
2. Phan Tien - Tanner model : Deborah number = 10 (tutorial)
3. Newtonian isothermal flow

Notations :

Psi : stream function
Stij : component ij of the stress tensor (cylindar coordinates)

1. Phan Tien - Tanner model : Deborah number = 1

Elapsed time =5400 s
Number of iterations = 12

Psi for De=10 Psi for newtonian case

St11 for De=10 St11 for newtonian case

St12 for De=10 St12 for newtonian case

2. Phan Tien - Tanner model : Deborah number = 10

TCPU = 1146 s
Elapsed time= 7059.7 s
Number of iterations = 17

3. Newtonian isothermal flow

TCPU = 3s
Elapsed time =21.6 s
Number of iterations = 1

Psi for De=10 Psi for De=1

Analysis

If we compare the three cases we can see that results for De=1 are closer to the newtonian case than for De=10. The deborah number described the state of the viscoelastic fluid :

• De<<1 viscous behaviour ( if De=0, this is a newtonian case )
• De>>1 elastic behaviour

Morover in the De=10 case, we can see the division into two parts of the flow separated by the stream line close to the wall before the contraction.