Meccanica

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Numerical simulations of an incompressible piezoviscous fluid flowing in a plane slider bearing

  • Martin Lanzendörfer
  • Josef Málek
  • Kumbakonam R. Rajagopal
Article
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Abstract

We provide numerical simulations of an incompressible pressure-thickening and shear-thinning lubricant flowing in a plane slider bearing. We study the influence of several parameters, namely the ratio of the characteristic lengths \(\varepsilon >0\) (with \(\varepsilon \searrow 0\) representing the Reynolds lubrication approximation); the coefficient of the exponential pressure–viscosity relation \(\alpha ^*\ge 0\); the parameter \(G^*\ge 0\) related to the Carreau–Yasuda shear-thinning model and the modified Reynolds number \({\mathrm {Re}}_\varepsilon \ge 0\). The finite element approximations to the steady isothermal flows are computed without resorting to the lubrication approximation. We obtain the numerical solutions as long as the variation of the viscous stress \(\varvec{S}=2\eta (p,{{\mathrm{tr}}}\,\varvec{D}^2)\varvec{D}\) with the pressure is limited, say \(|\partial \varvec{S}/\partial p|\le 1\). We show conclusively that the existing practice of avoiding the numerical difficulties by cutting the viscosity off for large pressures leads to results that depend sorely on the artificial cut-off parameter. We observe that the piezoviscous rheology generates pressure differences across the fluid film.

Keywords

Finite element approximation Incompressible fluid Pressure-thickening Shear-thinning Thin-film flow Channel flow Fluid mechanics 

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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Mathematical Institute, Faculty of Mathematics and PhysicsCharles UniversityPrague 8Czech Republic
  2. 2.Department of Mechanical EngineeringTexas A&M UniversityCollege StationUSA

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