An asymptotic analysis of the laminar-turbulent transition of yield stress fluids in pipes

Tim G. Myers; Sarah L. Mitchell; Paul Slatter

doi:10.1088/1742-6596/811/1/012007

An asymptotic analysis of the laminar-turbulent transition of yield stress fluids in pipes

Tim G. Myers
, Sarah L. Mitchell
, Paul Slatter

Research output: Contribution to journal › Conference article › peer-review

Abstract

The work in this paper concerns the axisymmetric pipe flow of a Herschel-Bulkley fluid, with the aim of determining a relation between the critical velocity (defining the transition between laminar and turbulent flow) and the pipe diameter in terms of the Reynolds number Re ₃. The asymptotic behaviour for large and small pipes is examined and simple expressions for the leading order terms are presented. Results are then compared with experimental data. A nonlinear regression analysis shows that for the tested fluids the transition occurs at similar values to the Newtonian case, namely in the range 2100 < Re ₃ < 2500.

Original language	English
Article number	012007
Journal	Journal of Physics: Conference Series
Volume	811
Issue number	1
DOIs	https://doi.org/10.1088/1742-6596/811/1/012007
Publication status	Published - 3 Mar 2017
Event	8th International Workshop on Multi-Rate Processes and Hysteresis, MURPHYS 2016 and 3rd International Workshop on Hysteresis and Slow-Fast Systems, HSFS 2016 - Barcelona, Spain Duration: 13 Jun 2016 → 17 Jun 2016

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10.1088/1742-6596/811/1/012007

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title = "An asymptotic analysis of the laminar-turbulent transition of yield stress fluids in pipes",

abstract = "The work in this paper concerns the axisymmetric pipe flow of a Herschel-Bulkley fluid, with the aim of determining a relation between the critical velocity (defining the transition between laminar and turbulent flow) and the pipe diameter in terms of the Reynolds number Re 3. The asymptotic behaviour for large and small pipes is examined and simple expressions for the leading order terms are presented. Results are then compared with experimental data. A nonlinear regression analysis shows that for the tested fluids the transition occurs at similar values to the Newtonian case, namely in the range 2100 < Re 3 < 2500.",

author = "Myers, \{Tim G.\} and Mitchell, \{Sarah L.\} and Paul Slatter",

note = "Publisher Copyright: {\textcopyright} Published under licence by IOP Publishing Ltd.; 8th International Workshop on Multi-Rate Processes and Hysteresis, MURPHYS 2016 and 3rd International Workshop on Hysteresis and Slow-Fast Systems, HSFS 2016 ; Conference date: 13-06-2016 Through 17-06-2016",

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T1 - An asymptotic analysis of the laminar-turbulent transition of yield stress fluids in pipes

AU - Myers, Tim G.

AU - Mitchell, Sarah L.

AU - Slatter, Paul

N1 - Publisher Copyright: © Published under licence by IOP Publishing Ltd.

PY - 2017/3/3

Y1 - 2017/3/3

N2 - The work in this paper concerns the axisymmetric pipe flow of a Herschel-Bulkley fluid, with the aim of determining a relation between the critical velocity (defining the transition between laminar and turbulent flow) and the pipe diameter in terms of the Reynolds number Re 3. The asymptotic behaviour for large and small pipes is examined and simple expressions for the leading order terms are presented. Results are then compared with experimental data. A nonlinear regression analysis shows that for the tested fluids the transition occurs at similar values to the Newtonian case, namely in the range 2100 < Re 3 < 2500.

AB - The work in this paper concerns the axisymmetric pipe flow of a Herschel-Bulkley fluid, with the aim of determining a relation between the critical velocity (defining the transition between laminar and turbulent flow) and the pipe diameter in terms of the Reynolds number Re 3. The asymptotic behaviour for large and small pipes is examined and simple expressions for the leading order terms are presented. Results are then compared with experimental data. A nonlinear regression analysis shows that for the tested fluids the transition occurs at similar values to the Newtonian case, namely in the range 2100 < Re 3 < 2500.

UR - https://www.scopus.com/pages/publications/85016318330

U2 - 10.1088/1742-6596/811/1/012007

DO - 10.1088/1742-6596/811/1/012007

M3 - Conference article

AN - SCOPUS:85016318330

SN - 1742-6588

VL - 811

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

IS - 1

M1 - 012007

T2 - 8th International Workshop on Multi-Rate Processes and Hysteresis, MURPHYS 2016 and 3rd International Workshop on Hysteresis and Slow-Fast Systems, HSFS 2016

Y2 - 13 June 2016 through 17 June 2016

ER -

An asymptotic analysis of the laminar-turbulent transition of yield stress fluids in pipes

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