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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 EngineerJeff.Bremer@jacobs.com

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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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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Agenda

• Theoretical Background

• Similarity Theory• Slatter Theory (used as a cross

check)• Results

• Conclusions / Questions

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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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Similarity Theory – How It works

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Similarity Theory – The Equations

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•

Similarity Theory – The Equations

Note : There is no requirement to define the underlying rheology

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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

Slatter Theory (1995) – The iterative approach

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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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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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Rheology Data

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

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Rheology Data

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

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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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Rheology Data

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Results – SG=1.75, prediction from 50NB Data

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Results – SG=1.70, prediction from 65NB Data

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Results – SG=1.65, prediction from 65NB Data

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Results – SG=1.60, prediction from 65NB Data

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Results – Problems with high density and small diameter

• Large Diameter forecasts are OK!!Slide 21

Results – Problems with high density and small diameter

• Large Diameter forecasts are OK!!Slide 22

Results – Problems with high density and small diameter

• Large Diameter forecasts are OK!!Slide 23

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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Questions

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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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