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Research Papers: Fundamental Issues and Canonical Flows

Drag-Reducing Flows in Laminar-Turbulent Transition Region

[+] Author and Article Information
Shu-Qing Yang, Donghong Ding

School of Civil, Mining
and Environmental Engineering,
Faculty of Engineering and Information Science,
University of Wollongong,
Northfields Avenue,
Wollongong, NSW 2522, Australia

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received January 22, 2013; final manuscript received April 13, 2014; published online July 24, 2014. Assoc. Editor: Mark F. Tachie.

J. Fluids Eng 136(10), 101202 (Jul 24, 2014) (9 pages) Paper No: FE-13-1035; doi: 10.1115/1.4027455 History: Received January 22, 2013; Revised April 13, 2014

This study makes an attempt to investigate Newtonian/non-Newtonian pipe flows in a laminar-turbulent transition region, which is an extraordinarily complicated process and is not fully understood. The key characteristic of this region is its intermittent nature, i.e., the flow alternates in time between being laminar or turbulent in a certain range of Reynolds numbers. The physical nature of this intermittent flow can be aptly described with the aid of the intermittency factor γ, which is defined as that fraction of time during which the flow at a given position remains turbulent. Spriggs postulated that a weighting factor can be used to calculate the friction factor, applying its values in laminar and turbulent states. Based on these, a model is developed to empirically express the mean velocity and Reynolds shear stress in the transition region. It is found that the intermittency factor can be used as a weighting factor for calculating the flow structures in the transition region. Good agreements can be achieved between the calculations and experimental data available in the literature, indicating that the present model is acceptable to express the flow characteristics in the transition region.

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Figures

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Fig. 1

Measured (symbols) and calculated (lines) velocity profiles in laminar, transition, and turbulent flow regions. For Re = 640, glucose syrup, γ¯t = 0 and D* = 1; for Re = 2700, 0.4% CMC, γ¯t = 0.75 and D* = 1.03; for Re = 3840, 0.2% PAA, γ¯t = 0.85 and D* = 1.09; for Re = 6600, 0.14% Carbopol 934, γ¯t = 0.99 and D* = 1.29; and for Re = 45,300, 0.09% CMC/0.09%XG, γ¯t = 1 and D* = 1.56.

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Fig. 2

Comparison of weighting factor determined from the measured friction factor with the intermittency factor, i.e., Eq. (10) and its modified form Eq. (21)

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Fig. 3

Friction factor versus Reynolds number in laminar-turbulent transition region based on Wójs's experimental data [46]

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Fig. 4

Friction factor versus Reynolds number based on Peixinho et al.'s [47] measurements

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Fig. 5

Friction factor versus Reynolds number in laminar-turbulent transition region based on Dou and Wang's [48] measurements

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Fig. 6

Turbulent intensity profiles measured by Peixinho et al. [47] and its comparison with Eq. (28)

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Fig. 7

Distribution of measured rms of streamwise velocity fluctuations in the laminar-turbulent transition region of Newtonian fluid flow

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Fig. 8

Distribution of measured rms of streamwise velocity fluctuations in the laminar-turbulent transition region of drag-reducing flow

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