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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