In the present work, a reduced-order method, “Proper Generalized Decomposition (PGD)” is extended and applied to the resolution of the Reynolds equation describing the behavior of the lubricant in hydrodynamic journal bearing. The PGD model is employed to solve the characteristic ‘Reynolds’ partial differential equation using the separation technique through the alternating direction strategy. The resulting separated-dimension system has a low computation cost compared to classical finite-difference resolution. Several numerical benchmark examples are investigated to verify the validity and accuracy of the proposed method. It has been found that numerical results obtained by the PGD method can achieve an improved convergence rate with a very low computation cost.
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@article{CRMECA_2016__344_10_689_0,
author = {Bilal Cherabi and Abderrachid Hamrani and Idir Belaidi and Sofiane Khelladi and Farid Bakir},
title = {An efficient reduced-order method with {PGD} for solving journal bearing hydrodynamic lubrication problems},
journal = {Comptes Rendus. M\'ecanique},
pages = {689--714},
publisher = {Elsevier},
volume = {344},
number = {10},
year = {2016},
doi = {10.1016/j.crme.2016.05.006},
language = {en},
}
TY - JOUR AU - Bilal Cherabi AU - Abderrachid Hamrani AU - Idir Belaidi AU - Sofiane Khelladi AU - Farid Bakir TI - An efficient reduced-order method with PGD for solving journal bearing hydrodynamic lubrication problems JO - Comptes Rendus. Mécanique PY - 2016 SP - 689 EP - 714 VL - 344 IS - 10 PB - Elsevier DO - 10.1016/j.crme.2016.05.006 LA - en ID - CRMECA_2016__344_10_689_0 ER -
%0 Journal Article %A Bilal Cherabi %A Abderrachid Hamrani %A Idir Belaidi %A Sofiane Khelladi %A Farid Bakir %T An efficient reduced-order method with PGD for solving journal bearing hydrodynamic lubrication problems %J Comptes Rendus. Mécanique %D 2016 %P 689-714 %V 344 %N 10 %I Elsevier %R 10.1016/j.crme.2016.05.006 %G en %F CRMECA_2016__344_10_689_0
Bilal Cherabi; Abderrachid Hamrani; Idir Belaidi; Sofiane Khelladi; Farid Bakir. An efficient reduced-order method with PGD for solving journal bearing hydrodynamic lubrication problems. Comptes Rendus. Mécanique, Volume 344 (2016) no. 10, pp. 689-714. doi : 10.1016/j.crme.2016.05.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2016.05.006/
[1] On the theory of lubrication and its application to mr. beauchamp tower's experiments, including an experimental determination of the viscosity of olive oil, Proc. R. Soc. Lond., Volume 40 (1886) no. 242–245, pp. 191-203
[2] Friction in machines and the effect of the lubricant, Inzherernii Zh., Volume 1 (1883), pp. 71-140
[3] First report on friction experiments, Proc. Inst. Mech. Eng., Volume 34 (1883) no. 1, pp. 632-659
[4] Friction and Lubrication in Mechanical Design, CRC Press, Boca Raton, 1998
[5] Theory of Hydrodynamic Lubrication, McGraw-Hill, New York, 1961
[6] Analytical Derivation and Experimental Evaluation of Short-Bearing Approximation for Full Journal Bearings, US Government Printing Office, Washington, D.C., USA, 1953
[7] Progress in fluid-film lubrication, Trans. Am. Soc. Mech. Eng., Volume 51 (1929) no. 2, pp. 153-163
[8] Zur hydrodynamischen Theorie der Schmiermittelreibung, Z. Math. Phys., Volume 50 (1904) no. 97, p. 155
[9] An exact analytical solution of the Reynolds equation for the finite journal bearing lubrication, Tribol. Int., Volume 55 (2012), pp. 46-58
[10] Evaluation of the finite journal bearing characteristics, using the exact analytical solution of the Reynolds equation, Tribol. Int., Volume 57 (2013), pp. 216-234
[11] A solution for the finite journal bearing and its application to analysis and design: I, ASLE Transact., Volume 1 (1958) no. 1, pp. 159-174
[12] Application of finite element methods to lubrication: an engineering approach, J. Tribol., Volume 94 (1972) no. 4, pp. 313-323
[13] 3d thermal steady-state CFD analysis of power friction losses in a turbocharger's journal bearing and comparison with finite difference method and experimentation, 12th EAEC, 2009
[14] A method for measuring the hydrodynamic effect on the bearing land, Tribol. Int., Volume 67 (2013), pp. 146-153
[15] Effect of number and size of recess on the performance of hybrid (hydrostatic/hydrodynamic) journal bearing, Proc. Eng., Volume 51 (2013), pp. 810-817
[16] Finite element method analysis of hydrodynamic journal bearing, Eur. J. Adv. Eng. Technology., Volume 2 (2015) no. 2, pp. 92-101
[17] Reduced order modeling of fluid/structure interaction, 2009 (Sandia National Laboratories Report, SAND No. 7189)
[18] Model Order Reduction: Theory, Research Aspects and Applications, vol. 13, Springer, 2008
[19] Model Order Reduction Techniques with Applications in Finite Element Analysis, Springer Science & Business, Media, 2013
[20] The proper orthogonal decomposition in the analysis of turbulent flows, Annu. Rev. Fluid Mech., Volume 25 (1993) no. 1, pp. 539-575
[21] An optimal projection method for the reduced-order modeling of incompressible flows, Comput. Methods Appl. Mech. Eng., Volume 200 (2011) no. 33, pp. 2507-2527
[22] A mathematical and numerical study of the sensitivity of a reduced order model by pod (rom–pod), for a 2d incompressible fluid flow, J. Comput. Appl. Math., Volume 270 (2014), pp. 522-530
[23] Nonlinear Computational Structural Mechanics, 1999
[24] Multiscale computational strategy with time and space homogenization: a radial-type approximation technique for solving microproblems, Int. J. Multiscale Comput. Eng., Volume 2 (2004) no. 4
[25] The Latin multiscale computational method and the proper generalized decomposition, Comput. Methods Appl. Mech. Eng., Volume 199 (2010) no. 21, pp. 1287-1296
[26] A short review on model order reduction based on proper generalized decomposition, Arch. Comput. Methods Eng., Volume 18 (2011) no. 4, pp. 395-404
[27] A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids, J. Non-Newton. Fluid Mech., Volume 139 (2006) no. 3, pp. 153-176
[28] A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modelling of complex fluids: part II: transient simulation using space-time separated representations, J. Non-Newton. Fluid Mech., Volume 144 (2007) no. 2, pp. 98-121
[29] On the simulation of kinetic theory models of complex fluids using the Fokker–Planck approach, Appl. Rheol., Volume 17 (2007) no. 2, p. 26494
[30] Proper general decomposition (pgd) for the resolution of Navier–Stokes equations, J. Comput. Phys., Volume 230 (2011) no. 4, pp. 1387-1407
[31] Proper generalized decomposition method for incompressible Navier–Stokes equations with a spectral discretization, Appl. Math. Comput., Volume 219 (2013) no. 15, pp. 8145-8162
[32] Non-incremental transient solution of the Rayleigh–Bénard convection model by using the pgd, J. Non-Newton. Fluid Mech., Volume 200 (2013), pp. 65-78
[33] Model reduction based on proper generalized decomposition for the stochastic steady incompressible Navier–Stokes equations, SIAM J. Sci. Comput., Volume 36 (2014) no. 3, p. A1089-A1117
[34] Hydrodynamic Lubrication: Bearings and Thrust Bearings, vol. 33, Elsevier, 1997
[35] Journal Bearings in Turbomachinery, Springer Science & Business Media, 2013
[36] Arnold Johannes Wilhelm Sommerfeld. 1868–1951, Obituary Notices of Fellows of the Royal Society, 1952, pp. 275-296
[37] Applied Parallel Computing: State of the Art in Scientific Computing, vol. 3732, Springer Science & Business Media, 2006
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