TITLE : TURBULENT CONCENTRIC ANNULAR FLOW OF POWER-LAW FLUIDS

BY : CHAM Development Team - G. Garnier

FOR : Validation of Turbulence & Non-Newtonian Models

PURPOSE OF THE CALCULATIONS:

• 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.