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Research Papers: Flows in Complex Systems

Pressure Drop Predictions for Laminar Fully-Developed Flows of Purely-Viscous Non-Newtonian Fluids in Circular Ducts

[+] Author and Article Information
Robert A. Brewster

CD-adapco,
60 Broadhollow Road, Melville, NY 11747
e-mail: robert.brewster@cd-adapco.com

Note that Eq. (3) of Brewster and Irvine [7] contains a typographical error and should read ηa = …

Contributed by the Fluids Engineering Division of ASME for publication in the Journal of Fluids Engineering. Manuscript received February 19, 2013; final manuscript received June 8, 2013; published online August 6, 2013. Assoc. Editor: Samuel Paolucci.

J. Fluids Eng 135(10), 101106 (Aug 06, 2013) (9 pages) Paper No: FE-13-1099; doi: 10.1115/1.4024790 History: Received February 19, 2013; Revised June 08, 2013

This paper provides the results of numerical calculations of pressure drops and centerline velocities for laminar fully-developed flows of non-Newtonian fluids in circular ducts. The particular non-Newtonian fluid model considered is the Cross model, which has shown the ability to model the behavior of time-independent purely-viscous fluids over a wide range of shear rates. It is shown that the Cross model is equivalent to the more recently proposed extended modified power law (EMPL) model, and an alternative formulation of the nondimensional parameters arising from the use of these models is explored. Results are presented for friction factors and nondimensional centerline velocities over a wide range of fluid and flow conditions, and it is shown that simpler constitutive models can be used in cases where the ratios of the limiting Newtonian viscosities are extreme. The implications of the results to the design and analysis of piping systems is considered, and simple and accurate correlations are provided for engineering calculations.

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References

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Figures

Grahic Jump Location
Fig. 1

Typical viscosity versus shear rate curve for a pseudoplastic (shear thinning) fluid —; and a dilatant (shear thickening) fluid - - -. Also indicated are the five shear rate regions: Region I—low shear rate Newtonian region; Region II—low shear rate transition region; Region III—power law region; Region IV—high shear rate transition region; Region V—high shear rate Newtonian region.

Grahic Jump Location
Fig. 4

Computed results for pseudoplastic EMPL fluids with P = 0.001: (a) f·ReM and (b) uc/u¯, as a function of B and n. Results for pseudoplastic MPL fluids are shown as dashed lines for comparison.

Grahic Jump Location
Fig. 3

Computed values of f·ReM for pseudoplastic EMPL fluids with P=10-12 (——), and results of Brewster and Irvine [7] for pseudoplastic MPL fluids (•). Note that the values plotted are for 1.e–4 ≤ B ≤ 0.9999.

Grahic Jump Location
Fig. 2

Computational grid mesh 1 (see Table 1)

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Fig. 5

Computed results for pseudoplastic EMPL fluids with P=0.001: (a) f·ReM and (b) uc/u¯, as a function of n for 0.9≤B≤1.0. Results for pseudoplastic Sisko fluids (see Appendix, Eq. (A6)) are shown as dashed lines for comparison.

Grahic Jump Location
Fig. 6

Computed results for pseudoplastic EMPL fluids with P=0.01: (a) f·ReM and (b) uc/u¯, as a function of B and n. Results for pseudoplastic MPL fluids are shown as dashed lines for comparison.

Grahic Jump Location
Fig. 7

Computed results for pseudoplastic EMPL fluids with P = 0.1: (a) f·ReM and (b) uc/u¯, as a function of B and n

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Fig. 8

Computed dimensionless (a) velocity and (b) shear rate profiles for EMPL fluids with B = 0.6. Curves for pseudoplastic (n < 1) fluids are for P = 0.1 and curves for dilatant fluids (n > 1) are for P = 10.

Grahic Jump Location
Fig. 9

Computed results for dilatant EMPL fluids with P = 1000: (a) f·ReM and (b) uc/u¯, as a function of B and n. Results for dilatant MPL fluids are shown as dashed lines for comparison.

Grahic Jump Location
Fig. 10

Computed results for dilatant EMPL fluids with: P = 10: (a) f·ReM and (b) uc/u¯, as a function of B and n

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