New insights on lubrication theory for compressible fluids

Document identifier: oai:DiVA.org:ltu-76138
Access full text here:10.1016/j.ijengsci.2019.103170
Keyword: Natural Sciences, Tribologi (ytteknik omfattande friktion, nötning och smörjning), Machine Elements, Asymptotic analysis, Dimension reduction, Navier–Stokes equations, Compressible flow, Reynold’s equation, Thin film approximation, Maskinteknik, Mathematics, Teknik och teknologier, Tribology (Interacting Surfaces including Friction, Lubrication and Wear), Mechanical Engineering, Engineering and Technology, Matematisk analys, Matematik, Naturvetenskap, Mathematical Analysis, Maskinelement
Publication year: 2019
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SDG 9 Industry, innovation and infrastructure
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Abstract:

The fact that the film is thin is in lubrication theory utilised to simplify the full Navier–Stokes system of equations. For incompressible and iso-viscous fluids, it turns out that the inertial terms are small enough to be neglected. However, for a compressible fluid, we show that the influence of inertia depends on the (constitutive) density-pressure relationship and may not always be neglected. We consider a class of iso-viscous fluids obeying a power-law type of compressibility, which in particular includes both incompressible fluids and ideal gases. We show by scaling and asymptotic analysis, that the degree of compressibility determines whether the terms governing inertia may or may not be neglected. For instance, for an ideal gas, the inertial terms remain regardless of the film height-to-length ratio. However, by means of a specific modified Reynolds number that we define we show that the magnitudes of the inertial terms rarely are large enough to be influential. In addition, we consider fluids obeying the well-known Dowson and Higginson density-pressure relationship and show that the inertial terms can be neglected, which allows for obtaining a Reynolds type of equation. Finally, some numerical examples are presented in order to illustrate our theoretical results.

Authors

Andreas Almqvist

Luleå tekniska universitet; Maskinelement
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Evgeniya Burtseva

Luleå tekniska universitet; Matematiska vetenskaper
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Francesc Pérez Ràfols

Luleå tekniska universitet; Maskinelement
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Peter Wall

Luleå tekniska universitet; Matematiska vetenskaper
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