Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent...
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Transcript of Jeff Bremer - Jacobs Engineering - Similarity Analysis and the Prediction of Laminar Turbulent...
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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