Detail publikačního výsledku

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

VACULA, J.; NOVOTNÝ, P.

Originální název

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

Anglický název

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

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

VACULA, J.; NOVOTNÝ, P.

Vydáno

30.06.2025

Nakladatel

MDPI

Místo

BASEL

ISSN

2075-4442

Periodikum

Lubricants

Svazek

13

Číslo

7

Stát

Švýcarská konfederace

Strany od

1

Strany do

19

Strany počet

19

URL

https://www.mdpi.com/2075-4442/13/7/293

Plný text v Digitální knihovně

http://hdl.handle.net/11012/255418

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",
  journal="Lubricants",
  year="2025",
  volume="13",
  number="7",
  pages="1--19",
  doi="10.3390/lubricants13070293",
  url="https://www.mdpi.com/2075-4442/13/7/293"
}

Dokumenty

lubricants-13-00293-v2