Tube flow of non‐Newtonian polymer solutions: Part II. Turbulent flow

Meter, Donald M.

doi:10.1002/aic.690100620

Cited by 29 publications

(7 citation statements)

References 12 publications

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“…polymer fluid flow through pipes in an industrial settings (Bird et al, 1987), capillary bundle model of a porous media (Savins, 1969), pore-Network model (Sochi and Blunt, 2008)). Amongst generalised Newtonian fluid models (Yilmaz and Gundogdu, 2008), Cross (Cross, 1965), Carreau (Yasuda, 1979), Carreau-Yasuda (Yasuda, 1979), Meter (Meter and Bird, 1964;Meter, 1964;Savins, 1969;Tsakiroglou, 2002;Tsakiroglou et al, 2003b,a), and Steller-Ivako model (Steller and Iwko, 2018) can predict S-shaped rheological properties (i.e. constant viscosity at low and high shear values and decreasing viscosity at intermediate shear values) of many shear-thinning fluids.…”

Section: Introductionmentioning

confidence: 99%

Effective viscosity and Reynolds number of non-Newtonian fluids using Meter model

2020

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The Meter model (a four-parameter model) captures shear viscosityshear stress relationship (S-shaped type) of polymeric non-Newtonian fluids. We devise an analytical solution for radial velocity profile, average velocity and volumetric flow rate of steady state laminar flow of non-Newtonian Meter model fluids through a circular geometry. The analytical solution converts to the Hagen-Posseuille equation for the Newtonian fluid case. We also develop the formulations to determine effective viscosity, Reynolds number and Darcy's friction factor using measurable parameters as available rheological models do not correctly define these parameters for a given set of flow condition in circular geometry. The analytical solution and formulations are validated against experimental data. The results suggest that the effective Reynolds number and effective friction factor estimated using the proposed formulation helps to characterise non-Newtonian fluid flow through a circular geometry in laminar and turbulent flow.

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Section: Introductionmentioning

confidence: 99%

Effective viscosity and Reynolds number of non-Newtonian fluids using Meter model

2020

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“…the eddy pair. The eddy pattern remains defined to the Although in several instances (10,22,24,28,39) drag outer edge of the sublayer and as these patterns may be reduction data have been correlated empirically and associated with about 50% of the total turbulent energy several theoretical analysis have been presented (11, 16, they must control to a large extent the radial momentum 41, 42) little consistent information, pertinent to the transport rates which exist in the wall region. From the processes involved in drag reduction, has evolved.…”

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confidence: 99%

Turbulence phenomena in drag reducing systems

1969

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An analysis based on the Townsend-Bakewell model of the eddies in the wall regions of turbulent shear flows shows that viscoelastic fluid properties must lead to significant reductions in the rate of production of turbulent energy. This analysis in turn leads to the proper form of the similarity laws for drag reducing fluids, heretofore deduced empirically.Measurements of the axial and radial turbulence intensities for flow through smooth round tubes are reported, as are measurements o f the time-averaged velocity profiles and the drag coefficients. These indicate that for solutions exhibiting drag reduction a t all Reynolds numbers the flow may be transitional to Reynolds numbers of the order of 105. This Design calculations based upon the present results suggest that in large diameter pipelines, or in boundary layers on large objects, drag reduction may not be attainable under conditions of practical interest until fluids having relaxation times an order of magnitude larger than those presently available, but with comparable viscosity levels, are developed or, alternately, until fluids exhibiting Weissenberg numbers which do not change with deformation rate, can be found.A growing number of studies have been undertaken cesses there. A recent detailed study of the Newtonian which aim to characterize or elucidate the physical asflow wit,hin this wall region (3) has shown that the large pects of drag reduction. Several of these (7, 14, 20, 24, eddies exist as counter-rotating pairs with their axes 35, 39, 46) include sufficient ranges of the primary varialong the mean flow direction. In the lateral direction a ables such as tube size, the polymeric additive used and diffuse influx of material occurs which is concentrated its concentration to illustrate the varied nature and extent between the two eddies and rapidly ejected from the of drag reduction and t,he difficulty of obtaining a genboundary layer region owing to the counter-rotation of era1 and quantitative understanding of the phenomenon. the eddy pair. The eddy pattern remains defined to the Although in several instances (10, 22, 24, 28, 39) drag outer edge of the sublayer and as these patterns may be reduction data have been correlated empirically and associated with about 50% of the total turbulent energy several theoretical analysis have been presented (11, 16, they must control to a large extent the radial momentum 41, 42) little consistent information, pertinent to the transport rates which exist in the wall region. From the processes involved in drag reduction, has evolved. Comstreamline patterns presented by Bakewell a graphical pounding this problem is the utility of measurements using analysis has shown (38) that the streamlines are adethe usual tools of research in turbulence, impact, and hotquately described by: wire probes, which has been severely questioned ( 2 , 15, 23, 25, 36) and remains in doubt for viscoelastic fluids. Thus the several experimental investigations in which such tools were employed ( 2 , 12, 13, 28, 44, 4 6 ) , though clea...

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“…A summary of the tremendous work done on drag reduction can be obtained from a number of comprehensive reviews on the subject (Lumley, 1969;Patterson et al, 1969;Gadd, 1971;Darby, 1972;Hoyt, 1972;Landahl, 1973;Lumley, 1973;Fisher and Ash, 1974;Palyvos, 1974;Virk, 1975;Shenoy, 1976;Ting, 1982;Shenoy, 1984). A number of empirical relationships for correlating and predicting drag reduction effects have been developed (Meter, 1964;Kilbane and Greenkorn, 1966;Seyer and Metzner, 1967;Virk et al, 1967). The correlations for drag-reducing fluids, which have in part a theoretical reasoning, are those of Meyer (1966), Seyer and Metzner (1969a), and Astarita et al (1969).…”

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confidence: 99%