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Research Papers: Hydrodynamic Lubrication

Large-Scale Simulation of Fluid Flows for Lubrication of Rough Surfaces

[+] Author and Article Information
Noel Brunetiere

Département GMSC,
Institut Pprime,
CNRS, Université de Poitiers, Ensma,
Futuroscope Chasseneuil Cedex 86962, France
e-mail: noel.brunetiere@univ-poitiers.fr

Q. Jane Wang

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60201
e-mail: qwang@northwestern.edu

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received February 4, 2013; final manuscript received June 21, 2013; published online September 23, 2013. Assoc. Editor: Daniel Nélias.

J. Tribol 136(1), 011701 (Sep 23, 2013) (14 pages) Paper No: TRIB-13-1037; doi: 10.1115/1.4024937 History: Received February 04, 2013; Revised June 21, 2013

This paper presents a novel method to compute the lubricant pressure distribution between a rough and a smooth surface in relative motion. The originality of this method is to combine a deterministic approach for the large scales and a stochastic model for the small scales of the problem. As a result, the new method allows a significant mesh reduction while maintaining an accurate prediction of the generated load.

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References

Figures

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Fig. 1

Configuration of the problem

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Fig. 2

Rough surfaces used in this study: (a) surface 1, L/λ = 64, (b) surface 2, L/λ = 32, (c) surface 3, L/λ = 16, and (d) surface 4, L/λ = 8

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Fig. 3

Power spectrum density (PSD) of a rough surface having an exponential autocorrelation function

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Fig. 5

Half profiles of the three filters in the x-direction: (a) spatial domain, and (b) frequency domain

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Fig. 6

Power spectral density in the x direction of the initial and filtered pressure fields (SC: sharp cut-off; TH: top-hat; and G: Gaussian)

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Fig. 7

Effect of the filter type and wave number cut-off on the pressure distribution for surface 3, p1 = p2 = 0, μVL/Sq2 = 16.9 MPa, h0 = 3 Sq: (a) sharp cut-off, kc = 8; (b) sharp cut-off, kc = 32; (c) top-hat, kc = 8; (d) top-hat, kc = 32; (e) Gaussian, kc = 8; (f) Gaussian, kc = 32; and (g) unfiltered pressure field

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Fig. 8

Effect of the frequency cut-off on the pressure statistics for surface 3, p1 = p2 = 0, μVL/Sq2 = 16.9 MPa, h0 = 3 Sq: (a) average pressure, and (b) RMS pressure

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Fig. 9

Correlation of the subgrid model results with the deterministic filtered ones in the x direction for surface 3, p1 = p2 = 0, μVL/Sq2 = 16.9 MPa, h0 = 3Sq: -(a) kc = 8, r = 0.83; and (b) kc = 32, r = 0.925

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Fig. 10

Correlation of the subgrid model results with the deterministic filtered ones in the y direction for surface 3, p1 = p2 = 0, μVL/Sq2 = 16.9 MPa, h0 = 3 Sq: (a) kc = 8, r = 0.834; and (b) kc = 32, r = 0.939

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Fig. 11

(a) Comparison of the measured and predicted subgrid roughness as a function of the frequency cut-off, and (b) the difference between the predicted (see Eq. (35)) and measured subgrid roughness as a function of the normalized frequency cut-off

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Fig. 12

Principle of the mesh degradation (for m = 2) for the deterministic and LSS approaches

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Fig. 13

Effect of the mesh density, expressed by kM(λ/L) on the generated load for p1 = p2 = 0 and μVL/Sq2 = 16.9 MPa: – (a) surface 1, h0 = 5 Sq; (b) surface 2, h0 = 3.5 Sq; (c) surface 3, h0 = 3 Sq; and (d) surface 4, h0 = 3 Sq

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Fig. 14

Effect of the mesh density, expressed by kM(λ/L) on the mass flow rate in the x direction, for p1 = p2 = 0 and μVL/Sq2 = 16.9 MPa: – (a) surface 1, h0 = 5 Sq; (b) surface 2, h0 = 3.5 Sq; (c) surface 3, h0 = 3 Sq; and (d) surface 4, h0 = 3 Sq

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Fig. 15

Comparison, for surface 4, of the coarse pressure fields to the “exact solution” shown by the bottom image: – (a) deterministic, nc = 16, kM(λ/L) = 2; (b) LSS, nc = 16, kM(λ/L) = 2; and (c) deterministic, n = 512, kM(λ/L) = 64

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Fig. 16

Comparison of the theoretical PSD to the real PSD of surface 3

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