0
Research Papers: Flows in Complex Systems

# Laminar-Turbulent Transition Flows of Non-Newtonian Slurries: Models Assessment

[+] Author and Article Information

Fluid Systems Engineering,
InnoTech Alberta Inc.,
Devon Research Centre,
1 Oil Patch Drive,
e-mail: kofifreeman@innotechalberta.ca

Martin Agelin-Chaab

Department of Automotive, Mechanical and
Manufacturing Engineering,
Faculty of Engineering and Applied Science,
University of Ontario Institute of Technology,
2000 Simcoe Street North,
e-mail: martin.agelin-chaab@uoit.ca

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received May 13, 2017; final manuscript received June 4, 2018; published online June 29, 2018. Assoc. Editor: M'hamed Boutaous.

J. Fluids Eng 141(1), 011104 (Jun 29, 2018) (10 pages) Paper No: FE-17-1275; doi: 10.1115/1.4040503 History: Received May 13, 2017; Revised June 04, 2018

## Abstract

In this study, a qualitative assessment of transitional velocity engineering models for predicting non-Newtonian slurry flows in a horizontal pipe was performed using data from a wide range of pipe diameters (25–268 mm). In addition, the gamma theta transition model was used to compute selected flow conditions. These models were used to predict transitional velocities in large pipe diameters (up to 420 mm) for slurries. In general, it was observed that most of the current engineering models predict transitional velocities conservatively. Based on the gamma theta transition model results, for large Hedström numbers (He $≳$ 105), other methods should be used to predict transitional velocities if a change in the pipe diameter (scale-up) results in an order of magnitude increase in the He value. It was also found that the gamma theta transition model predicted a laminar flow condition in the fully developed region for flow conditions with a small plug region (low-yield stress-to-wall shear stress ratio), which is contrary to what has been observed in some experiments. This is attributed to the local fluid rheological parameters values, which might be different from those reported. However, the gamma theta transition model results are in good agreement with the experimental data for flow conditions that have a large plug region (high-yield stress-to-wall shear stress ratio).

<>

## References

Xu, J. , Gillies, R. , Small, M. , and Shook, C. , 1993, “ Laminar and Turbulent Flow of Kaolin Slurries,” Hydrotransport, 12, pp. 595–613.
Slatter, P. T. , and Wasp, E. J. , 2000, “ The Laminar-Turbulent Transition in Large Pipes,” Tenth International Conference on Transport and Sedimentation of Solid Particles, Wroclaw, Poland, Sept. 4–7, pp. 389–399.
Wilson, K. C. , and Thomas, A. D. , 2006, “ Analytic Model of Laminar‐Turbulent Transition for Bingham Plastics,” Can. J. Chem. Eng., 84(5), pp. 520–526.
Van den Heever, E. , 2013, “ Rheological Model Influence on Pipe Flow Predictions for Homogeneous Non-Newtonian Fluids,” M.S. thesis, Cape Peninsula University of Technology, Cape Town, South Africa.
Graham, L. J. , Pullum, L. , and Wu, J. , 2016, “ Flow of Non‐Newtonian Fluids in Pipes With Large Roughness,” Can. J. Chem. Eng., 94(6), pp. 1102–1107.
Kabwe, C. , Haldenwang, R. , Fester, V. , and Chhabra, R. , 2017, “ Transitional Flow of Non-Newtonian Fluids in Open Channels of Different Cross-Sectional Shapes,” J. Braz. Soc. Mech. Sci. Eng., 39(6), pp. 1–19.
Gharib, N. , Bharathan, B. , Amiri, L. , McGuinness, M. , Hassani, F. P. , and Sasmito, A. P. , 2017, “ Flow Characteristics and Wear Prediction of Herschel‐Bulkley Non‐Newtonian Paste Backfill in Pipe Elbows,” Can. J. Chem. Eng., 95(6), pp. 1181–1191.
McFarlane, A. J. , Addai-Mensah, J. , and Bremmell, K. , 2005, “ Rheology of Flocculated Kaolinite Dispersions,” Korea-Australia Rheol. J., 17(12), pp. 181–190.
Hammad, K. J. , 2016, “ The Flow and Decay Behavior of a Submerged Shear-Thinning Jet With Yield Stress,” ASME J. Fluids Eng., 138(8), p. 081205.
Malin, M. R. , 1997, “ The Turbulent Flow of Bingham Plastic Fluids in Smooth Circular Pipes,” Int. J. Heat Mass Transfer, 6(6), pp. 793–804.
Güzel, B. , Frigaard, I. , and Martinez, D. M. , 2009, “ Predicting Laminar–Turbulent Transition in Poiseuille Pipe Flow for Non-Newtonian Fluids,” Chem. Eng. Sci., 64(2), pp. 254–264.
Sutherland, A. , Haldenwang, R. , Chhabra, R. , and van den Heever, E. , 2015, “ Selecting the Best Rheological and Pipe Turbulent Flow Prediction Models for Non-Newtonian Fluids-Use of RMSE and R2 Vs. AIC,” 17th International Conference on Transport and Sedimentation of Solid Particles, Delft, The Netherlands, Sept. 22–25, pp. 317–326.
Liu, W.-J. , Burgess, K. , Roudnev, A. , and Bootle, M. , 2009, “ Pumping Non-Newtonian Slurries,” Tech. Bull., Weir Miner. Div., 14(2), pp. 1–4.
Swamee, P. K. , and Aggarwal, N. , 2011, “ Explicit Equations for Laminar Flow of Bingham Plastic Fluids,” J. Pet. Sci. Eng., 76(3–4), pp. 178–184.
Hedström, B. O. A. , 1952, “ Flow of Plastics Materials in Pipes,” Ind. Eng. Chem., 44(3), pp. 651–656.
Shook, C. A. , and Roco, M. C. , 1991, Slurry Flow: Principles and Practice, Butterworth-Heinemann, Boston, MA.
Shook, C. A. , Gillies, R. G. , and Sanders, R. S. , 2002, Pipeline Hydrotransport With Applications in Oilsand Industry, Saskatchewan Research Council, Saskatoon, SK, Canada.
Menter, F. R. , 1994, “ Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications,” AIAA J., 32(8), pp. 1598–1605.
Wilcox, D. C. , 1988, “ Multiscale Model for Turbulent Flows,” AIAA J., 26(11), pp. 1311–1320.
Menter, F. R. , Langtry, R. B. , Likki, S. R. , Suzen, Y. B. , Huang, P. G. , and Völker, S. , 2006, “ A Correlation Based Transition Model Using Local Variables—Part 1: Model Formulation,” ASME J. Turbomach., 128(3), pp. 413–422.
Langtry, R. B. , Menter, F. R. , Likki, S. R. , Suzen, Y. B. , Huang, P. G. , and Völker, S. , 2006, “ A Correlation Based Transition Model Using Local Variables—Part 2: Test Cases and Industrial Applications,” ASME J. Turbomach., 128(3), pp. 423–434.
Langtry, R. B. , and Menter, F. R. , 2005, “ Transition Modeling for General CFD Applications in Aeronautics,” AIAA Paper No. 2005-522.
Adane, K. F. K. , Shah, S. I. A. , and Sanders, R. S. , 2012, “ Numerical Study of Liquid-Liquid Vertical Dispersed Flows,” ASME Paper No. FEDSM2012-72377.
Antaya, C. L. , Adane, K. F. K. , and Sanders, R. S. , 2012, “ Modelling Concentrated Slurry Pipeline Flows,” ASME Paper No. FEDSM2012-72379.
Hashemi, S. A. , Spelay, R. B. , Adane, K. F. , and Sanders, R. S. , 2016, “ Solids Velocity Fluctuations in Concentrated Slurries,” Can. J. Chem. Eng., 94(6), pp. 1059–1065.
Barth, T. J. , and Jesperson, D. C. , 1989, “ The Design and Application of Upwind Schemes on Unstructured Meshes,” AIAA Paper No. 89-0366.
Litzenberger, C. G. , 2003, “ Rheological Study of Kaolin Clay Slurries,” M.S thesis, University of Saskatchewan, Saskatoon, SK, Canada.
Spelay, R. B. , 2007, “ Solids Transport in Laminar, Open Channel Flow of Non-Newtonian Slurries,” Ph.D. thesis, University of Saskatchewan, Saskatoon, SK, Canada.
Peixinho, J. , Nouar, C. , Desaubry, C. , and Théron, B. , 2005, “ Laminar Transitional and Turbulent Flow of Yield Stress Fluid in a Pipe,” J. Non-Newtonian Fluid Mech., 128(2–3), pp. 172–184.
Rudman, M. , Graham, L. J. , Blackburn, H. M. , and Pullum, L. , 2002, “ Non-Newtonian Turbulent and Transitional Pipe Flow,” 15th Hydrotransport, Banff, AB, Canada, June 3–5, pp. 271–286.
Esmael, A. , and Nouar, C. , 2008, “ Transitional Flow of a Yield-Stress Fluid in a Pipe: Evidence of a Robust Coherent Structure,” Phys. Rev. E, 77(5 Pt 2), p. 057302.

## Figures

Fig. 1

Illustration of the intersection method. Data points from Wilson and Thomas [3].

Fig. 5

Iso-contour plots of normalized velocity differences (laminar velocities minus transition velocities), Δu/U at U = 2.0 m/s in a 158 mm diameter pipe for fluid prepared from water and 17%v/v kaolin

Fig. 6

Comparison of pressure drop in a 53 mm diameter pipe for fluid prepared from water and 22.6%v/v kaolin with 0.03 wt.% TSPP of kaolin

Fig. 7

Comparison of pressure drop in a 158 mm diameter pipe for fluid prepared from water and 17%v/v kaolin

Fig. 4

GTM normalized velocity (u/U) profiles in a 158 mm diameter pipe for fluid prepared from water and 17%v/v kaolin

Fig. 8

Comparison of (a) velocity profiles in a fully developed region and (b) the turbulent intermittency along the streamwise direction at y/D = 0.1 in 53 mm [28] and 158 mm [1] diameter pipes

Fig. 9

Iso-contour plots of the turbulent intermittency for various pipe diameters using water and 9% bentonite slurry by van den Heever [4]

Fig. 2

Transition velocity versus the Hedström number

Fig. 3

Parity plot of transition velocities from prediction and experiments

## Errata

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections

• TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
• EMAIL: asmedigitalcollection@asme.org