Stabilised computations for viscoelastic flows under compressible implementations

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

doi:10.1016/j.jnnfm.2005.12.003

Cited by 27 publications

(42 citation statements)

References 42 publications

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“…In these situations, compressibility effects may become very important. As noted by Belblidia et al [12], there are a number of advantages in working with compressible flow, e.g. the compatibility of discrete function spaces.…”

Section: Introductionmentioning

confidence: 99%

On the effects of a compressible viscous lubricant on the load‐bearing capacity of a journal bearing

Bollada

Phillips

2007

Numerical Methods in Fluids

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SUMMARYA compressible viscous isothermal model is presented for studying journal-bearing lubrication. The viscosity in the model thickens with increasing density. The governing equations are written in terms of velocity, the natural logarithm of the density and the kinematic extra-stress tensor. A semi-Làgrangian treatment of the material derivatives is combined with a spectral element discretization in space. The roles of the speed of sound and the eccentricity ratio on the load-bearing capacity of the journal bearing are investigated. Compressibility is shown to enhance the load-bearing capacity and this effect is amplified as the eccentricity ratio approaches unity. It is shown that for speeds of sound in the region of those of multigrade oils, the dominant component of the force on the journal acts along the line joining the centres of the bearing and journal and in the direction away from the narrow gap.

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Section: Introductionmentioning

confidence: 99%

On the effects of a compressible viscous lubricant on the load‐bearing capacity of a journal bearing

Bollada

Phillips

2007

Numerical Methods in Fluids

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“…Belblidia et al [1] considered an extension of this model to fluids with a solvent component and obtained a compressible Oldroyd B model. The equation of motion is…”

Section: Model B (Belblidia Et Al [1])mentioning

confidence: 99%

“…is commonly referred to as the augmented pressure (see for example [1]). In general flows,p will differ from p, but within an incompressible context which one of the two quantities is adopted is irrelevant.…”

Section: Introductionmentioning

confidence: 99%

“…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%

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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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“…Several authors developed in the past unified computational methods for compressible and incompressible viscous flows [24][25][26][27][28][29][30], showing results for a wide range of flow speeds, but in two-dimensional simple geometries. Extensions of low to vanishing Mach number compressible flows to viscoelastic constitutive models have been studied by Webster and co-workers [32,33,31] in a very comprehensive work, and were compared to experimental results in [34]. However, these studies were devoted to two-dimensional flows.…”

Section: Introductionmentioning

confidence: 99%

A new three-dimensional mixed finite element for direct numerical simulation of compressible viscoelastic flows with moving free surfaces

et al. 2011

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The original publication is available at http://www.springer.comInternational audienceTA Mixed Finite Element (MFE) method for 3D non-steady flow of a viscoelastic compressible fluid is presented. It was used to compute polymer injection flows in a complex mold cavity, which involves moving free surfaces. The flow equations were derived from the Navier-Stokes incompressible equations, and we extended a mixed finite element method for incompressible viscous flow to account for compressibility (using the Tait model) and viscoelasticity (using a Pom-Pom like model). The flow solver uses tetrahedral elements and a mixed velocity/pressure/extra-stress/density formulation, where elastic terms are solved by decoupling our system and density variation is implicitly considered. A new DEVSS-like method is also introduced naturally from the MINI-element formulation. This method has the great advantage of a low memory requirement. At each time slab, once the velocity has been calculated, all evolution equations (free surface and material evolution) are solved by a space-time finite element method. This method is a generalization of the discontinuous Galerkin method, that shows a strong robustness with respect to both re-entrant corners and flow front singularities. Validation tests of the viscoelastic and free surface models implementation are shown, using literature benchmark examples. Results obtained in industrial 3D geometries underline the robustness and the efficiency of the proposed method

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Stabilised computations for viscoelastic flows under compressible implementations

Cited by 27 publications

References 42 publications

On the effects of a compressible viscous lubricant on the load‐bearing capacity of a journal bearing

On the effects of a compressible viscous lubricant on the load‐bearing capacity of a journal bearing

On the Mathematical Modelling of a Compressible Viscoelastic Fluid

A new three-dimensional mixed finite element for direct numerical simulation of compressible viscoelastic flows with moving free surfaces

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