Encyclopaedia Index

### TITLE : TURBULENT PIPE FLOW OF POWER-LAW FLUIDS

BY : CHAM Development Team - M R Malin

FOR : Validation of Turbulence & Non-Newtonian Models

DATE : 1996 PHOENICS Version : 2.2.1

### 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 pipes.

• 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 flow of Power-law in pipes is relevant in the many engineering applications, especially within the manufacturing and process industries.

• Calculations are made to calculate the frictional resistance, along with the fully-developed velocity profile, for both laminar and turbulent flow by use of the single-slab solver.

• The turbulence is represented by use of a modified version of the Lam-Bremhorst low-Re k-e model.

• The parameters are: the Fanning friction factor f; the power-law index n; and the Generalised Reynolds number:

```        Re=rho*{Wb**(2-n)}*{D**n}/({8**(n-1)}*{(0.75+0.25/n)**n}*K).
```
where K is the consistency, D is the pipe diameter, and Wb the bulk velocity.
1. FRICTIONAL RESISTANCE
2. LAMINAR FLOW: MEAN-VELOCITY PROFILES
3. TURBULENT FLOW: MEAN-VELOCITY PROFILES
4. TURBULENT FLOW: MEAN VELOCITY PROFILES
5. TURBULENT FLOW: LOGARITHMIC MEAN VELOCITY PROFILES

wbs