jeff bremer - jacobs engineering - similarity analysis and the prediction of laminar turbulent...
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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/1xvoBPTTRANSCRIPT
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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 [email protected]
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.
Slide 2
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
Slide 3
Agenda
• Theoretical Background
• Similarity Theory• Slatter Theory (used as a cross
check)• Results
• Conclusions / Questions
Slide 4
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
Slide 5
Similarity Theory – How It works
Slide 6
Similarity Theory – The Equations
Slide 7
•
Similarity Theory – The Equations
Note : There is no requirement to define the underlying rheology
Slide 8
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
Slide 10
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.
Slide 11
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
Slide 12
Rheology Data
• Data was in the form of pressure-gradient plots and Pseudo-shear charts
Slide 13
Rheology Data
• Data was in the form of pressure-gradient plots and Pseudo-shear charts
Slide 14
Rheology Data
• Pseudo-shear charts transformed using the Rabinowitsch-Mooney Equation to obtain true shear rates to infer Bingham Plastic Rheology
Slide 15
Rheology Data
Slide 16
Results – SG=1.75, prediction from 50NB Data
Slide 17
Results – SG=1.70, prediction from 65NB Data
Slide 18
Results – SG=1.65, prediction from 65NB Data
Slide 19
Results – SG=1.60, prediction from 65NB Data
Slide 20
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.
Slide 24
Questions
Slide 25
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.
Slide 26