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Advanced Simulation & Analysis, Becthel Nuclear, Security & Environmental(1)
CD-adapco™,(2)
Joel Peltier1, Andri Rizhakov
1, Brigette Rosendall
1,
Nathanael Inkson2, Simon Lo
2
Evaluation of RANS Modeling
of Non-Newtonian Bingham
Fluids in the Turbulence
Regime using STAR-CCM+®
CIVIL
GOVERNMENT SERVICES
MINING & METALS
OIL, GAS & CHEMICALS
POWER
Contents
Motivation
Scope
Theory and Background
Implementation
– Using STAR-CCM+ capturing mean shear rates
– Tying small scale shear rates to mean field variables
Comparison with data
Future Work
Why does non-Newtonian Turbulent Flow
Matter?
Applications
Pipeline transport of slurries, drilling mud & sewage sludge
Polymer processing (with drag-reduction applications)
Transport of biological fluids (blood flow)
Pulse jet mixers for slurries
Publications
Escudier, M.P., Poole, R. J., Presti, F., Dales, C., Nouar, C., Desaubry, C., Graham, L.,
and L. Pullum;: Observations of asymmetrical flow behavior in transitional pipe flow of
yield-stress and other shear-thinning liquids.
Pinho, F. T. and J.H. Whitelaw: Flow of non-Newtonian Fluids in an Pipe
Bartoski, A.: Application of Rehological Models in Prediction of Turbulent Slurry Flows
Rudman, M. and Blackburn, H.M.: Direct numerical simulation of turbulent non-Newtonian
flow using a spectral element method
Malin, M.R.: Turbulent flow of Bingham Plastic fluids in smooth circular tubes
Meyer P.A., Kurath, D.E. and C.W. Stewart: “Overview of the Pulse Jet Mixer Non-
Newtonian Scaled Test Program
Why Bechtel is interested
Processing of solids containing waste
Non-Newtonian at high solids content
Bingham-Plastic behavior
Turbulent jet mixing
© Bechtel | 4
Scope of this Study
Reynolds-Averaged Navier-Stokes (RANS) turbulence modeling for
Herschel-Bulkley fluids
© Bechtel | 5
Herschel-Bulkley Rheology Bingham Plastic Rheology
• Shear Stress, 𝜏
• Shear Rate, 𝛾
• Yield stress, 𝜏𝑌• Consistency, 𝐾
• Power-law index, 𝑛.
𝜏 = 𝜏𝑌 + 𝐾 𝛾𝑛 𝜏 = 𝜏𝑌 + 𝐾 𝛾
Why hasn't RANS Modeling of Herschel-Bulkley Fluids Matured?
© Bechtel | 6
Turbulence
Energy
Spectrum
𝛾 ~1
ℓ 𝛾 ~
1
𝜂
Energy-
Containing
RangeInertial
Range
Dissipation
Range
Herschel-Bulkley Rheology
depends on
High Shear-Rate Events
RANS Captures
Mean Shear
Rates
𝛾
ℓ = characteristic large scale length 𝜂= Kolmogorov length scale
Theory Extending RANS Modeling to Herschel-Bulkley Fluids
© Bechtel | 7
From Tennekes, H., 1968: Simple Model for the
Small-Scale Structure of Turbulence, Phys.
Fluids, 11 (33), 669-671.
• The characteristic large-scale length, ℓ, and velocity, 𝑞, scales are provided by RANS.
• At high Re, ℓ ≫ 𝜂
• Vortex stretching reduces ℓ in to 𝜂
• Small-scale shear rates, then, may be characterized by
• Tennekes’ description of inertial-range theory accounting for small-scale intermittency provides the tie between small-scale shear rates and mean-field variables from RANS.
𝛾 ~𝑞
𝜂
Implementation of a RANS Model for
Turbulence in a Herschel-Bulkley Fluid
© Bechtel | 8
Setup a
Newtonian flow
turbulence model Override the dynamic viscosity with a field function
for the apparent viscosity, 𝜇𝐴
Estimate the small-scale 𝛾 from ℓ and 𝑞
Estimate 𝜇𝐴 using 𝜇𝐴 =𝜏
𝛾=
𝜏𝑌
𝛾+ 𝐾 𝛾(𝑛−1)
Run the turbulence model, as normal
Assumptions
• The Newtonian turbulence model allows
spatially varying viscosities
• The Newtonian turbulence model
asymptotes to zero turbulence in low
Reynolds number regimes
Implementation of the turbulence
model modification for Herschel-
Bulkley fluids in STAR-CCM+ is
straight-forward.
Comparison Experiment
© Bechtel | 9
Pipe length: 12 m
Pipe ID: 100 ± 0.4 mm
Fully developed flow, varying Re (ranging from laminar to transition to turbulent)
Measurement location,
120D from pipe inlet
• Velocity measurements from Dantec Fiber Flow LDA
• Rheological data from Bohlin VOR controlled stress rheometer
• Aqueous solution of 1.5 wt% Laponite
𝜏 = 𝜏𝑌 + 𝐾( 𝛾)𝑛, 𝜏 > 𝜏𝑌 (Herschel–Bulkley model)
𝜏𝑌 𝑃𝑎 = 4.42, 𝐾 𝑃𝑎 𝑠𝑛 = 0.242, 𝑛 = 0.534
Experimental Comparison Data
© Bechtel | 10
CFD Model
© Bechtel | 11
inflow Periodic domain w/ pressure drop0.5 m
outflow
50 mm
Mesh:
- Axi-symmetric
- 2000 cells
- 15 prism layers
Physics:
- RANS
- Realizable k-epsilon turbulence
- Two-layer all y+ wall treatment
- Field functions modify viscosity to Non-
Newtonian rheology
Numerics:
- Implicit unsteady
- 2nd order time & space
symmetry
CFD Model Results
© Bechtel | 12
Re = Turbluent
Fluid flow
regime case
Re = Transitional
Re = Laminar
Viscosity (Pa·s)
Comparison of Bechtel Model CFD
Results to Experiment
© Bechtel | 13
Comparison of STAR-CCM+ Preliminary
Model CFD Results to Experiment
© Bechtel | 14
Summary
A turbulence model extension to Herschel-Bulkley
non-Newtonian fluids is proposed
– Instantaneous local is the key instead of the volume averaged
approach
The model has been benchmarked against
experimental pipe flow data across a range spanning
laminar, transitional, and fully turbulent conditions.
Next steps:
– Test in jet-mixing environment
– Test with solid-liquid mixtures, i.e. Eulerian-Granular models.
© Bechtel | 15