nach oben

Rheologica Acta

Erschienen in:

21.07.2020 | Original Contribution

An efficient algorithm of solution for the flow of generalized Newtonian fluid in channels of simple geometries

verfasst von: Michal Wrobel

Erschienen in: Rheologica Acta | Ausgabe 9/2020

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

In this paper a problem of stationary flow of generalized Newtonian fluid in a thin channel is considered. An efficient algorithm of solution is proposed that includes a flexible procedure for a continuous approximation of the apparent viscosity by means of elementary functions combined with analytical integration of the governing equations. The algorithm can be easily adapted to circular or elliptic conduits. The accuracy and efficiency of computations are analyzed using an example of the Carreau fluid. The proposed computational scheme proves to be highly efficient and versatile providing excellent accuracy of solution at a very low computational cost.

Vorheriger Artikel Rheology of aqueous foams under pressure

Nächster Artikel Rheological behavior of water-clay suspensions under large amplitude oscillatory shear

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Nur mit Berechtigung zugänglich

The superscript ‘g’ will be used throughout this paper to denote the general form of apparent viscosity.

Abulencia J, Theodore L (2009) Fluid flow for the practicing chemical engineer. Wiley, New York. ISBN 9780470423851CrossRef

Akbar N, Nadeem S (2014) Carreau fluid model for blood flow through a tapered artery with a stenosis. Ain Shams Eng J 5(4):1307–1316CrossRef

Bird R, Armstrong R, Hassager O (1987) Dynamics of polymeric liquids, vol 1. Wiley, New York

Brujan E (2011) Cavitation in non-Newtonian fluids: with biomedical and bioengineering applications. Springer, Berlin. ISBN: 3642153429CrossRef

Busch A, Myrseth V, Khatibi M, Skjetne P, Hovda S, Johansen S (2018) Rheological characterization of polyanionic cellulose solutions with application to drilling fluids and cuttings transport modeling. Appl Rheol 28(2):25154

Carreau P, De Kee D, Chhabra R (1997) Rheology of polymeric systems principles and applications. Hanser/Gardner Publications, Munich

Clarion M, Deegan M, Helton T, Hudgins J, Monteferrante N, Ousley E, Armstrong M (2018) Contemporary modeling and analysis of steady state and transient human blood rheology. Rheol Acta 57(2):141–168CrossRef

de Castro A, Radilla G (2017) Flow of yield stress and Carreau fluids through rough-walled rock fractures: prediction and experiments. Water Resour Res 53(7):6197–6217CrossRef

Gholipour A, Ghayesh M, Zander A (2018) Nonlinear biomechanics of bifurcated atherosclerotic coronary arteries. Int J Eng Sci 133:60–83CrossRef

Kim S (2018) Flow-rate based method for velocity of fully developed laminar flow in tubes. J Rheol 62:1379–1407CrossRef

Kim S (2019) Flow rate based framework for solving viscoplastic flow with slip. J Non-Newton Fluid 269:37–46CrossRef

Kim N, Reddy J (2019) 3-D least-squares finite element analysis of flows of generalized Newtonian fluids. J Non-Newton Fluid 266:143–159CrossRef

Kozicki W, Chou C, Tiu C (1966) Non-Newtonian flow in ducts of arbitrary cross-sectional shape. Chem Eng Sci 21(8):665–679CrossRef

Laun H (2003) Pressure dependent viscosity and dissipative heating in capillary rheometry of polymer melts. Rheol Acta 42:295–308CrossRef

Lavrov A (2015) Flow of truncated power-law fluid between parallel walls for hydraulic fracturing applications. J Non-Newton Fluid 223:141–146CrossRef

Mitsoulis E, Tsamopoulos J (2016) Numerical simulations of complex yield-stress fluid flows. Rheol Acta 56(3):231–258CrossRef

Moukhtari F, Lecampion B (2018) A semi-infinite hydraulic fracture driven by a shear-thinning fluid. J Fluid Mech 838:573–605CrossRef

Osiptsov A (2017) Fluid mechanics of hydraulic fracturing: a review. J Petrol Sci Eng 156:513–535CrossRef

Peck D, Wrobel M, Perkowska M, Mishuris G (2018a) Fluid velocity based simulation of hydraulic fracture: a penny shaped model—part I: the numerical algorithm. Meccanica 53(15):3615–3635CrossRef

Peck D, Wrobel M, Perkowska M, Mishuris G (2018b) Fluid velocity based simulation of hydraulic fracture—a penny shaped model. Part II: new, accurate semi-analytical benchmarks for an impermeable solid. Meccanica 53(15):3637–3650CrossRef

Perkowska M (2016) Mathematical and numerical modeling of hydraulic fractures for non-Newtonian fluids. PhD thesis, Aberystwyth University

Perkowska M, Wrobel M, Mishuris G (2016) Universal hydrofracturing algorithm for shear–thinning fluids: particle velocity based simulation. Comput Geotech 71:310–337CrossRef

Perlacova T, Prusa V (2015) Tensorial implicit constitutive relations in mechanics of incompressible non-Newtonian fluids. J Non-Newton Fluid 216:13–21CrossRef

Rubenstein D, Yin W, Frame M (2015) Biofluid mechanics, 2nd edn. Academic, New York

Rubin A (1995) Propagation of magma filled cracks. Annu Rev Earth Planet Sci 23:287–336CrossRef

Ruschak K, Weinstein S (2013) A local power-law approximation to a smooth viscosity curve with application to flow in conduits and coating dies. polym eng sci 54(10):2301–2309CrossRef

Sochi T (2014) Using Euler-lagrange variational principle to obtain flow relations for generalized Newtonian fluids. Rheol Acta 53(1):15–22CrossRef

Sochi T (2015) Analytical solutions for the flow of Carreau and Cross fluids in circular pipes and thin slits. Rheol Acta 54(8):745–756CrossRef

Wrobel M (2020) On the application of simplified rheological models of fluid in the hydraulic fracture problems. Int J Eng Sci 150:103275CrossRef

Wrobel M, Mishuris G, Piccolroaz A (2017) Energy release rate in hydraulic fracture: can we neglect an impact of the hydraulically induced shear stress. Int J Eng Sci 111:28–51CrossRef

Wrobel M, Mishuris G, Piccolroaz A (2018) On the impact of tangential traction on the crack surfaces induced by fluid in hydraulic fracture: response to the letter of A.M. Linkov. Int J Eng Sci 127:217–219. Int J Eng Sci 127:220–224CrossRef

Titel: An efficient algorithm of solution for the flow of generalized Newtonian fluid in channels of simple geometries
verfasst von: Michal Wrobel
Publikationsdatum: 21.07.2020
Verlag: Springer Berlin Heidelberg
Erschienen in: Rheologica Acta / Ausgabe 9/2020
Print ISSN: 0035-4511
Elektronische ISSN: 1435-1528
DOI: https://doi.org/10.1007/s00397-020-01228-2

Premium Partner

Marktübersichten

Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.

Zur Marktübersicht

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Technik"

Springer Professional "Wirtschaft+Technik"

Weitere Artikel der Ausgabe 9/2020

Rheology of aqueous foams under pressure

Rheological behavior of water-clay suspensions under large amplitude oscillatory shear

The influence of polypropylene-block/graft-polycaprolactone copolymers on melt rheology, morphology, and dielectric properties of polypropylene/polycarbonate blends

Correction to: Rheological behavior of water-clay suspensions under large amplitude oscillatory shear

Elongational behavior of silica nanoparticle-filled low-density polyethylene/polylactic acid blends and their morphology

Re-entrant solid behavior of 3D-printable epoxy inks

Premium Partner

Marktübersichten