Computation of weakly‐compressible highly‐viscous liquid flows

Webster, M.F.; Keshtiban, I.J.; Belblidia, Fawzi

doi:10.1108/02644400410565306

Cited by 15 publications

(13 citation statements)

References 54 publications

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“…Taliadorou et al (2008) simulated the extrusion of strongly compressible Newtonian liquids and found that compressibility can lead to oscillatory steady-state free surfaces. Webster et al (2004) introduced numerical algorithms for solving weakly compressible, highly viscous laminar Newtonian flows at low Mach numbers. They applied their methods to the driven cavity and the contraction flow problems.…”

Section: Introductionmentioning

confidence: 99%

Laminar axisymmetric flow of a weakly compressible viscoelastic fluid

2011

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The combined effects of weak compressibility and viscoelasticity in steady, isothermal, laminar axisymmetric Poiseuille flow are investigated. Viscoelasticity is taken into account by employing the Oldroyd-B constitutive model. The fluid is assumed to be weakly compressible with a density that varies linearly with pressure. The flow problem is solved using a regular perturbation scheme in terms of the dimensionless isothermal compressibility parameter. The sequence of partial differential equations resulting from the perturbation procedure is solved analytically up to second order. The two-dimensional solution reveals the effects of compressibility and the other dimensionless numbers and parameters in the flow. Expressions for the average pressure drop, the volumetric flow rate, the total axial stress, as well as for the skin friction factor are also derived and discussed. The validity of other techniques used to obtain approximate solutions of weakly compressible flows is also discussed in conjunction with the present results.

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Section: Introductionmentioning

confidence: 99%

Laminar axisymmetric flow of a weakly compressible viscoelastic fluid

2011

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“…This finally results in no change in mean density due to compression and the flow becomes incompressible in the limit, irrespective of the fact that there may still be some large density variations due to non-homogeneous entropy distributions. This necessitates a modified solver algorithm with Mach-uniform accuracy and efficiency, applicable to both compressible and incompressible regimes inside a flow device [3][4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Large Eddy Simulation of acoustic pulse propagation and turbulent flow interaction in expansion mufflers

Singh

Rubini

2015

Applied Acoustics

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“…Edwards and Beris [5] adopt a weakly compressible framework so the issue is perhaps not as pertinent there. Webster et al [19] use the static pressure, but in later papers adopt the use of augmented pressure in the equation of state (see [1,9]), presumably recognising that augmented pressure,p, has more physical significance than static pressure, p, within a dynamic setting. Of course, in an isotropic fluid at equilibrium in a region containing a free surface, the two pressure fields are equal since the isotropic part of the extra stress vanishes.…”

Section: Introductionmentioning

confidence: 99%

On the Mathematical Modelling of a Compressible Viscoelastic Fluid

Bollada

Phillips

2012

Arch Rational Mech Anal

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Article:Bollada, PC and Phillips, TN (2012) ReuseUnless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version -refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher's website. TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. On the Mathematical Modelling of a Compressible Viscoelastic FluidThe fundamental principles associated with the development of mathematical models for compressible viscoelastic fluids are described using methodology and examples, that are sometimes conflicting, from the literature. The modelling of compressibility introduces two additional issues that need to be addressed over those that are required for incompressible fluids. The first issue is concerned with the role of variable density in the derivation of viscoelastic constitutive equations. The second, and perhaps more controversial issue, is concerned with the definition of pressure in a compressible setting, where it is seen to be dependent on bulk viscosity. A heuristic derivation of a compressible version of the Upper Convected Maxwell (UCM) model, starting from first principles in elasticity continuum mechanics, is presented, which suggests a dependence between dynamic viscosity and bulk viscosity, thereby addressing both issues.

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Computation of weakly‐compressible highly‐viscous liquid flows

Cited by 15 publications

References 54 publications

Laminar axisymmetric flow of a weakly compressible viscoelastic fluid

Laminar axisymmetric flow of a weakly compressible viscoelastic fluid

Large Eddy Simulation of acoustic pulse propagation and turbulent flow interaction in expansion mufflers

On the Mathematical Modelling of a Compressible Viscoelastic Fluid

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