Encyclopaedia Index

### TITLE : TURBULENT PIPE FLOW OF BINGHAM PLASTICS

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 models and non-Newtonian models for the flow of Bingham- plastic fluids in pipes.

• Bingham plastic fluids are time-independent viscous fluids for which the apparent viscosity decreases with shear rate, and motion only commences when the yield stress is exceeded.

• The flow of Bingham plastics in pipes is of relevance in the transport of granular suspensions, slurries, sewage sludge, muds and paints.

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

• The turbulence is represented by use of two different low-Re turbulence models, namely: the Lam-Bremhorst k-e model and the Wilcox k-w model.

• Computations are performed for fully-developed laminar and turbulent flow.

• The parameters are: the Fanning friction factor f; the Bingham Reynolds number Re=rho*Wb*D/K, and the Hedstrom number, He=Y*Re, where Y is the Yield number defined by Y=Tauy*D/(K*Wb) where Tauy is the yield stress, K is the consistency, D is the pipe diameter, and Wb the bulk velocity.

1. FRICTIONAL RESISTANCE: LAM-BREMHORST LOW-RE K-E MODEL
2. FRICTIONAL RESISTANCE: WILCOX LOW-RE K-W MODEL
3. MEAN VELOCITY PROFILES FOR BENTONITE SLURRIES
4. MEAN VELOCITY PROFILES FOR ALUMINA-WATER SLURRIES
5. MEAN VELOCITY PROFILES AT VARIOUS HEDSTROM NUMBERS FOR RE=1E5
6. VARIATION OF TRANSITIONAL RE WITH HEDSTROM NUMBER

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