Flow of non‐newtonian fluids—correlation of the laminar, transition, and turbulent‐flow regions

Metzner, A. B.; Reed, Jason

doi:10.1002/aic.690010409

Cited by 909 publications

(369 citation statements)

References 9 publications

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“…The quantity f exp calculated from experimental data on pressure loss is sometimes called the Fanning friction factor 6 . (11) in which f theo is the friction factor estimated theoretically and Re mr is the Reynolds number defined by METZNER and REED 18 . By using the Power-Law model for simple ducts, such as the circular pipe, it is possible to analytically solve the momentum equation and to obtain the generalized Reynolds number defined by METZNER and REED 18 : (12) in which K is the consistency index (Pa.s n ) and n is the flow behavior index (dimensionless).…”

Section: Evaluation Of Friction Factors In Pipe Flowmentioning

confidence: 99%

Rheological and thermophysical properties of blackberry juice

Cabral¹,

Orrego²,

Gabas³

et al. 2007

Ciênc. Tecnol. Aliment.

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Rheological and thermophysical properties were determined for blackberry juice, which was produced from blackberry fruit at 9.1 0.5°Brix and density of 1.0334 0.0043 g cm -3 . The concentration process was performed using a roto evaporator, under vacuum, to obtain concentrated juice at about 60 °Brix. In order to obtain different concentrations, concentrated juice was diluted with distilled water. Rheological measurements were carried out using a Rheotest 2.1 Searle type rheometer. In the tested ranges, the samples behaved as pseudoplastic fluids, and the PowerLaw model was satisfactorily fitted to the experimental data. The friction factor was measured for blackberry juice in laminar flow conditions of pseudoplastic behavior. Thermal conductivity, thermal diffusivity and density of blackberry juice at 9.4 to 58.4 °Brix were determined, in triplicate, at 0.5 to 80.8 °C. Polynomial regression was performed to fit experimental data obtaining a good fit. Both temperature and concentration showed a strong influence on thermophysical properties of blackberry juice. Calculated apparent specific heat values varied from 2.416 to 4.300 kJ.kg -1 °C in the studied interval. Keywords: fruit juice; rheology; thermal conductivity; thermal properties. ResumoAs propriedades reológicas e termofísicas foram determinadas para suco de amora produzido a partir da fruta com 9.1 0.5 °Brix e densidade de 1,0334 0,0043 g cm -3 . O processo de concentração foi realizado utilizando-se um roto evaporador, sob vácuo, obtendo-se o suco concentrado em aproximadamente 60 °Brix. As diferentes concentrações foram obtidas a partir da diluição do suco concentrado em água destilada. As medidas reológicas foram conduzidas utilizando-se o reômetro Rheotest 2.1 do tipo Searle. Em todos os experimentos as amostras apresentaram um comportamento pseudoplástico, e o modelo da Lei da Potência foi ajustado satisfatoriamente aos dados experimentais. O fator de atrito foi medido para o suco em regime laminar com comportamento pseudoplástico. A condutividade térmica, a difusividade térmica e a densidade foram determinadas em triplicata para o suco de amora nas faixas de 9,4 a 58,4 °Brix e de 0,5 a 80,8 °C.A temperatura e a concentração mostraram forte influência nas propriedades termofísicas do suco de amora. Os valores do calor específico aparente variaram de 2,416 a 4,300 kJ.kg -1 °C. Palavras-chave: condutividade térmica; propriedades térmicas; reologia; suco de fruta.

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Section: Evaluation Of Friction Factors In Pipe Flowmentioning

confidence: 99%

Rheological and thermophysical properties of blackberry juice

Cabral¹,

Orrego²,

Gabas³

et al. 2007

Ciênc. Tecnol. Aliment.

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“…where the appropriate Reynolds number for non-Newtonian fluids is defined as follows: [21] Re MR ¼ Du m r m m app ð4Þ…”

Section: Flow Characterization Of Emulsions In Pipesmentioning

confidence: 99%

Rheological behaviour of oil and water emulsions and their flow characterization in horizontal pipes

Zhang

2016

Can J Chem Eng

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In this work, the rheological behaviour of oil and water emulsions and their flow characterization were studied using a Haake RS6000 rheometer and a lab scale flow loop. The rheological properties of the synthetic emulsions were investigated at oil volume fractions from 0.1-1.0 L/L and shear rates from 0.001-1000 s À1 at a system temperature of 20 8C. The emulsions flow, formed by the SMV static mixer installed before the test section, was observed in the 2-m long horizontal pipes with 25 and 50 mm inner diameters at different mixture flow rates from 0.01-7.00 m 3 /h. A comparison between rheological measurements and laminar flow data shows that the values of the Sauter mean droplet diameters formed by the SMV static mixer are approximately one order of magnitude bigger than those measured by the rheometer. For oil-in-water emulsions with low oil content, the stress-strain relationships obtained in the rheometer are more suitable for predicting the transport characteristics of the emulsions with a large pipe diameter than those with a small pipe diameter. In addition, the phase inversion points in the pipe flow are closer to those measured at high shear rates in the rheometer. Therefore, the apparent viscosity obtained by the rheology measurements at high shear rates could be introduced for accurate calculations of the mixture Reynolds number and the friction factor in emulsions flow.

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“…From the works of Metzner and Reed (1955) and Kozicki et al (1966) it follows that the generalised viscosity, g g , for the flow of power-law fluids in ducts of arbitrary cross-section can be defined as (Delplace and Leuliet, 1995;Gut and Pinto, 2003;Carezzato et al, 2007):…”

Section: Introductionmentioning

confidence: 99%

“…where u is the mean velocity, D H the hydraulic diameter, g(n) a hyperbolic function of n and K a geometrical parameter given by the product of the Fanning friction factor, f, and the Reynolds number, Re g , for a Newtonian fluid under laminar flow conditions (Metzner and Reed, 1955;Delplace and Leuliet, 1995):…”

Section: Introductionmentioning

confidence: 99%

Friction factors of power-law fluids in chevron-type plate heat exchangers

Fernandes

Dias

Nóbrega

et al. 2008

Journal of Food Engineering

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a b s t r a c tIn the present work laminar flows of Newtonian and power-law fluids through cross-corrugated chevrontype plate heat exchangers (PHEs) are numerically studied in terms of the geometry of the channels. The plates area enlargement factor was a typical one (1.17), the corrugation angle, b, varied between 30°and 60°and the flow index behaviour, n, between 0.25 and 1. Single friction curves fRe g = K for both Newtonian and non-Newtonian fluids are proposed for each b by developing an adequate definition of the generalised Reynolds number, Re g . The coefficient K compares well with experimental data, for all (seven) values of b, and depends on the tortuosity coefficient, s. It was found that, for each b, s decreases with the decrease of n. Food fluids are frequently processed in PHEs and usually behave as non-Newtonian fluids. This study can be useful in engineering applications as well as in the characterization of transport phenomena in PHEs.

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Flow of non‐newtonian fluids—correlation of the laminar, transition, and turbulent‐flow regions

Cited by 909 publications

References 9 publications

Rheological and thermophysical properties of blackberry juice

Rheological and thermophysical properties of blackberry juice

Rheological behaviour of oil and water emulsions and their flow characterization in horizontal pipes

Friction factors of power-law fluids in chevron-type plate heat exchangers

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