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www.jacobs.com | worldwide Similarity analysis and the prediction of laminar-turbulent transition in a non- Newtonian slurry 4TH ANNUAL SLURRY PIPELINES CONFERENCE – PERTH WESTERN AUSTRALIA. 11-12 NOVEMBER 2014 Jeff Bremer, PhD, FIEAust | Jacobs Principal Engineer [email protected]

Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent Transition in a non-Newtonian Slurry

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The 4th Annual Slurry Pipelines Conference is the world's only event wholly dedicated to the operational challenges, design questions, innovations, pumps and tailings related to slurry pipelines in the mining and resources sectors. For more information on the event, please visit: http://bit.ly/1xvoBPT

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Page 1: Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent Transition in a non-Newtonian Slurry

www.jacobs.com | worldwide

Similarity analysis and the prediction of laminar-turbulent transition in a non-Newtonian slurry4TH ANNUAL SLURRY PIPELINES CONFERENCE – PERTH WESTERN AUSTRALIA. 11-12 NOVEMBER 2014

Jeff Bremer, PhD, FIEAust | Jacobs Principal [email protected]

Page 2: Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent Transition in a non-Newtonian Slurry

Background

• Newcrest’s Cadia Valley Operations(CVO) are in Orange NSW.

• Twinned DN630 tailings lines were decoupled and upgraded in 2013/2014

• Jacobs was engaged to do the design. Started with rheology, and need to forecast head loss and the L-T transition.

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Page 3: Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent Transition in a non-Newtonian Slurry

Pipe Loop Tests – carried out by Coffey Mining in 2010

• Five pipe sizes

• 40NB,50NB3,65NB, 80NB and 100NB

• Four slurry densities

• SG=1.75, 1.7, 1.65 and 1.6

• Flow and pressure data analysed by Jacobs

Analysis by Jacobs - 2013

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Page 4: Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent Transition in a non-Newtonian Slurry

Agenda

• Theoretical Background

• Similarity Theory• Slatter Theory (used as a cross

check)• Results

• Conclusions / Questions

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Page 5: Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent Transition in a non-Newtonian Slurry

Pipe Loop Test Data

Laminar-Turbulent (L-T) transition

• Pressure gradient vs flow rate in the pipe is transformed into a pseudo shear chart.

• Turbulence is detected when there is a sudden change in slope of the curve

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Page 6: Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent Transition in a non-Newtonian Slurry

Similarity Theory – How It works

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Page 7: Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent Transition in a non-Newtonian Slurry

Similarity Theory – The Equations

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Page 8: Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent Transition in a non-Newtonian Slurry

Similarity Theory – The Equations

Note : There is no requirement to define the underlying rheology

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Page 9: Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent Transition in a non-Newtonian Slurry

Similarity Theory – applies to non-Newtonian fluids

RHS is independent of D

Can use µeq for a non-Newtonian Fluid

Only stress at the pipe wall counts and the equations work equally well for non-Newtonian fluidsSlide 9

Page 10: Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent Transition in a non-Newtonian Slurry

Slatter Theory (1995) – The iterative approach

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Page 11: Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent Transition in a non-Newtonian Slurry

Slatter Theory (1995) – The iterative approach

Solution requires an initial guess of the wall shear stress and iterative calculation of the plug diameter and velocity until Re3 = 2100 is achieved.

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Page 12: Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent Transition in a non-Newtonian Slurry

Slatter and Wasp (2004) – Simplified Formula

This approach is VERY much quicker than the iterative solution

It is still based on Slatter’s Reynolds Re3 number but uses correlation to data

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Page 13: Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent Transition in a non-Newtonian Slurry

Rheology Data

• Data was in the form of pressure-gradient plots and Pseudo-shear charts

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Page 14: Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent Transition in a non-Newtonian Slurry

Rheology Data

• Data was in the form of pressure-gradient plots and Pseudo-shear charts

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Page 15: Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent Transition in a non-Newtonian Slurry

Rheology Data

• Pseudo-shear charts transformed using the Rabinowitsch-Mooney Equation to obtain true shear rates to infer Bingham Plastic Rheology

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Page 16: Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent Transition in a non-Newtonian Slurry

Rheology Data

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Page 17: Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent Transition in a non-Newtonian Slurry

Results – SG=1.75, prediction from 50NB Data

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Page 18: Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent Transition in a non-Newtonian Slurry

Results – SG=1.70, prediction from 65NB Data

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Page 19: Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent Transition in a non-Newtonian Slurry

Results – SG=1.65, prediction from 65NB Data

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Page 20: Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent Transition in a non-Newtonian Slurry

Results – SG=1.60, prediction from 65NB Data

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Page 21: Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent Transition in a non-Newtonian Slurry

Results – Problems with high density and small diameter

• Large Diameter forecasts are OK!!Slide 21

Page 22: Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent Transition in a non-Newtonian Slurry

Results – Problems with high density and small diameter

• Large Diameter forecasts are OK!!Slide 22

Page 23: Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent Transition in a non-Newtonian Slurry

Results – Problems with high density and small diameter

• Large Diameter forecasts are OK!!Slide 23

Page 24: Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent Transition in a non-Newtonian Slurry

Conclusions

• Similarity Laws and Slatter’s Theory are powerful tools for predicting the L-T transition velocity.

• No need to understand rheology to predict using similarity laws.

• The closed form Slatter-Wasp formulae ,e.g.Vc = 26 y. For He . 1.5 x

105 are easy to use and give the same results (within 5%) as the iterative calculation.

• Slatter theory over predicted Vc in smaller pipes in this study, but was very accurate at larger sizes. The data was un-calibrated and sample size small. Hence the “effect” may simply be experimental error.

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Page 25: Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent Transition in a non-Newtonian Slurry

Questions

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Page 26: Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent Transition in a non-Newtonian Slurry

References

• 1. Slatter, P. T. (1995, 24-26 January). Turbulent flow of non-Newtonian slurries in pipes. Paper presented at the 8th International Conference on Transport and Sedimentation of Solid Particles, Prague.

• 2. Slatter, P. T. (1999). Role of rheology in the pipelining of mineral slurries. Mineral Processing and Extractive Metallurgy Review, 20(1), 281-300.

• 3. Barenblatt, G. I., Chorin, A. J., & Prostokishin, V. M. (1997). Scaling laws for fully developed turbulent flow in pipes. Applied Mechanics Reviews, 50(7), 413-429.

• 5. Wilson, K. C., Addie, G. R., Sellgren, A., & Clift, R. (Eds.). (2006). Slurry transport using centrifugal pumps (Third Edition). Boston: Springer.

• 6. Slatter, P. T., & Wasp, E. J. (2000, 4-7 September). The laminar/turbulent transition in large pipes. Paper presented at the 10th International Conference on Transport and Sedimentation of Solid Particles, Wroclaw.

• 8. Slatter, P. T., & Wasp, E. J. (2002, September). Yield stress - How low can you go?Paper presented at the 11th Conference on Transport and Sedimentation of Solid Particles, Ghent.

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