BY : CHAM Development Team - G. Garnier

FOR : Validation of Turbulence & Non-Newtonian Models

- The main objective of the calculations is to validate the low-Re
turbulence model and non-Newtonian model for the flow of Power-
Law fluids in concentric annuli.
- Power-law fluids are time-independent viscous fluids for which
the shear stress is related to the deformation rate by the
consistency index K and the power-law index n. For n<1, the
fluid is pseudoplastic (shear thinning), and for n>1, it is
dilitant (shear thickening). If n=1, the fluid is Newtonian.
- The parameters are :
_ Rin : inner radius _ Rout: outer radius _ n : Power-law index _ K : consistency index _ Rho : density _ Pump rate

- The turbulence is represented by use of a modified version of
the Lam-Bremhorst low-Re k-e model. This modification had been
made for the turbulent pipe flow of power-law fluids so that
the predicted friction factor become in better agreement with
the one given by the Dodge-Metzner correlation [4].
- The predicted pressure drops are compared with experimental data
[2] (fig. 1) and the Reed correlation [1] (fig. 2).
- Typically, the calculations utilise 220 radial grid cells, with the
grid spacing increasing in geometric progression from the both walls.
The progression ratio is 1.05, and the near-wall grid node is located
at y+{=rho*w**(2-n)y**n/K}=0.5 where w{=(tauw/rho)**.5} is the friction
velocity and tauw the average wall shear stress.
- The stress is put on the importance of the location of this near-wall
grid node (y+=.5). A more refined grid with more cells and near-wall
grid nodes closer to the wall gives worse predicted pressure drops.
This condition is to be stricly followed if one wants reliable computed
results.
- Predicted pressure drops are systematically from 5 until 8 percent lower
than data, which is the accuracy of any experimental data or turbulent
correlation. But the comparison with other correlations (Frederickson
and Bird correlation [3], for instance) has shown that the predicted
pressure drops are always lower than the ones given by the correlation.
This could suggest a new correction in the Lam-Bremhorst low-Re k-e model.
- References.
[1,2] Troy Reed and Alex Sas-Jaworsky, "Flow of power law fluids in eccentric annuli, 4th International Conference on Coiled Tubing Technology, March 4-7, 1996. [1]: figure 2. [2]: figure 4.

[3] A. H. P. Skelland, "Non-Newtonian Flow and Heat Transfer",1967 pp 224-225.

[4] Mike R. Malin, "Turbulent pipe flow of power law fluids.", PHOENICS application album, 1996.

2. REED CORRELATION: PRESSURE vs PUMP RATE