Publication detail

On the Influence of the Convective Term in the Navier–Stokes Equation on the Forces in Hydrodynamic Bearings

VACULA, J. NOVOTNÝ, P.

English title

On the Influence of the Convective Term in the Navier–Stokes Equation on the Forces in Hydrodynamic Bearings

Type

journal article in Web of Science

Language

en

Original abstract

Many theories describing the flow of viscous fluids in thin lubrication layers during rotor motion inside a stator, including the influence of the convective term in the Navier–Stokes equation, are known and widely used. However, the results of individual studies show some inconsistencies in evaluating the influence of the convective term on the force occurring in the lubrication layer. Here, the effect of the convective term on the force acting on an arbitrarily moving rotor is explained based on a theoretical analysis of the Navier–Stokes equation. It is shown that for a constant fluid density in the case of an arbitrary trajectory of the centre of a non-rotating rotor, the convective term has zero effect on the force on the rotor. A non-zero effect of the convective term may only arise as a result of the spatial distribution of the momentum density at the inlet and outlet surfaces of the lubricating layer or as a result of variable fluid density due to cavitation or the compressibility of the fluid. Thus, the theoretical discussion presented here clarifies the numerical solutions obtained by researchers in the field of hydrodynamic lubrication and allows us to understand the reasons for the numerical behaviour of some simplified models.

English abstract

Many theories describing the flow of viscous fluids in thin lubrication layers during rotor motion inside a stator, including the influence of the convective term in the Navier–Stokes equation, are known and widely used. However, the results of individual studies show some inconsistencies in evaluating the influence of the convective term on the force occurring in the lubrication layer. Here, the effect of the convective term on the force acting on an arbitrarily moving rotor is explained based on a theoretical analysis of the Navier–Stokes equation. It is shown that for a constant fluid density in the case of an arbitrary trajectory of the centre of a non-rotating rotor, the convective term has zero effect on the force on the rotor. A non-zero effect of the convective term may only arise as a result of the spatial distribution of the momentum density at the inlet and outlet surfaces of the lubricating layer or as a result of variable fluid density due to cavitation or the compressibility of the fluid. Thus, the theoretical discussion presented here clarifies the numerical solutions obtained by researchers in the field of hydrodynamic lubrication and allows us to understand the reasons for the numerical behaviour of some simplified models.

Keywords in English

hydrodynamic bearing; inertial forces; lubrication theory; Navier–Stokes equation

Released

30.06.2025

Publisher

MDPI

Location

BASEL

ISSN

2075-4442

Volume

13

Number

7

Pages from–to

1–19

Pages count

19

BIBTEX


@article{BUT198490,
  author="Jiří {Vacula} and Pavel {Novotný},
  title="On the Influence of the Convective Term in the Navier–Stokes Equation on the Forces in Hydrodynamic Bearings",
  year="2025",
  volume="13",
  number="7",
  month="June",
  pages="1--19",
  publisher="MDPI",
  address="BASEL",
  issn="2075-4442"
}