Numerical research of the infinitely wide wedge flow based on the lattice Boltzmann method

Abstract

A new computational fluid dynamics method, the incompressible lattice Boltzmann method (LBM) is utilized to simulate fluid flow of the infinitely wide wedge in this paper. Compared with the traditional method, LBM is a mesoscopic scale method and some characteristics can be described more clearly with LBM. In this article, three kinds of model .i.e. linear type, parabolic type and harmonic type wedge models are built. The streamline and velocity contour in the fluid field are described. The pressure distribution of different types wedge is studied in LBM. The results manifest that, for the same bottom boundary velocity, the parabolic type and harmonic type wedges are easy to form a vortex, and the load capacity in the harmonic type wedge model is the largest. This paper is ready to investigate the microscopic lubrication mechanism of journal bearing in the future.

Keywords

LBM microscopic mechanism fluid flow pressure distribution

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References

Pinkus O and Sternlicht B. Theory of hydrodynamic lubrication. New York: McGraw-Hill, 1961.

Curzon

Series expansions for the dimensionless load capacity per unit width of a plane infinite slider bearing. Tribol Int 1982; 15: 191–192.

Visnadi

De Castro

HF.

Influence of bearing clearance and oil temperature uncertainties on the stability threshold of cylindrical journal bearings. Mech Mach Theor 2019; 134: 57–73.

Lin

Chang

Derivation of dynamic couple-stress Reynold’s equation of sliding-squeezing surfaces and numerical solution of plane inclined slider bearings. Tribol Int 2003; 36: 679–685.

Shyu

S-H

Hsu

W-C.

A numerical study on the negligibility of cross-film pressure variation in infinitely wide plane slider bearing, Rayleigh step bearing and micro-grooved parallel slider bearing. Int J Mech Sci 2018; 137: 315–323.

Gao

Yin

Jiang

, et al. Analysis on design parameters of water-lubricated journal bearings under hydrodynamic lubrication. Proc IMechE, Part J: J Engineering Tribology 2016; 230: 1019–1029.

Chen

Sun

Cao

Investigations on influence of groove shapes for the journal bearing in high-speed and heavy-load press system. Ind Lubricat Tribol 2018; 70: 230–240.

Oladeinde

Akpobi

JA.

A comparative study of load capacity and pressure distribution of infinitely wide parabolic and inclined slider bearings. In: Alexander M Korsunsky (ed.) Proceedings of the world congress on engineering. London, UK, 30 June--2 July 2010, pp.1370–1377.

Das

NC.

A study of optimum load capacity of slider bearings lubricated with power law fluids. Tribol Int 1999; 32: 435–441.

10.

Benzi

Succi

Vergassola

The lattice Boltzmann equation: theory and applications. Phys Rep 1992; 222: 145–197.

11.

Chen

Doolen

GD.

Lattice Boltzmann method for fluid flows. Annu Rev Fluid Mech 1998; 30: 329–364.

12.

Zhang

Lattice Boltzmann method for microfluidics: models and applications. Microfluid Nanofluid 2011; 10: 1–28.

13.

Aidun

Clausen

JR.

Lattice-Boltzmann method for complex flows. Annu Rev Fluid Mech 2010; 42: 439–472.

14.

Huang

Pan

Numerical simulation of viscous flow over a grooved surface by the lattice Boltzmann method. J Shanghai Jiaotong Univ (Sci) 2016; 21: 143–150.

15.

Brenner

Al-Zoubi

Mukinovic

, et al. Numerical simulation of surface roughness effects in laminar lubrication using the lattice-Boltzmann method. J Tribol 2007; 129: 603–610.

16.

Kucinschi

Afjeh

AA.

A lattice-Boltzmann approach to fluid film lubrication. J Tribol 2010; 132: 021705.

17.

Ding

Shi

Luo

Numerical simulation of viscous flow over non-smooth surfaces. Comput Math Appl 2011; 61: 3703–3710.

18.

Luo

Lattice Boltzmann model for the incompressible Navier–Stokes equation. J Stat Phys 1997; 88: 927–944.

19.

Guo

Zheng

Shi

Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method. Chin Phys 2002; 11: 366.

20.

Guo

Zheng

Shi

An extrapolation method for boundary conditions in lattice Boltzmann method. Phys Fluids 2002; 14: 2007–2010.

21.

Zhang

Shi

Chai

Lattice Boltzmann simulation of lid-driven flow in trapezoidal cavities. Comput Fluids 2010; 39: 1977–1989.

22.

Petra

BM.

Advanced modelling of elastohydrodynamic lubrication. PhD Dissertation, Imperial College, London, 2005.