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New insights on lubrication theory for compressible fluids
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.ORCID-id: 0000-0001-7029-1112
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.ORCID-id: 0000-0003-1963-6829
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.ORCID-id: 0000-0002-3556-328x
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.ORCID-id: 0000-0001-8211-3671
2019 (engelsk)Inngår i: International Journal of Engineering Science, ISSN 0020-7225, E-ISSN 1879-2197, Vol. 145, artikkel-id 103170Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

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.

sted, utgiver, år, opplag, sider
Elsevier, 2019. Vol. 145, artikkel-id 103170
Emneord [en]
Thin film approximation, Reynold’s equation, Compressible flow, Navier–Stokes equations, Dimension reduction, Asymptotic analysis
HSV kategori
Forskningsprogram
Maskinelement; Matematik
Identifikatorer
URN: urn:nbn:se:ltu:diva-76138DOI: 10.1016/j.ijengsci.2019.103170ISI: 000496842000009Scopus ID: 2-s2.0-85072601607OAI: oai:DiVA.org:ltu-76138DiVA, id: diva2:1355166
Merknad

Validerad;2019;Nivå 2;2019-09-27 (johcin)

Tilgjengelig fra: 2019-09-27 Laget: 2019-09-27 Sist oppdatert: 2019-12-09bibliografisk kontrollert

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Almqvist, AndreasBurtseva, EvgeniyaRàfols, Francesc PérezWall, Peter

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