Skip to main content Accessibility help

Homogenization of a compressible cavitation model



We develop a mathematical model in hydrodynamic lubrication that takes into account three phenomena: cavitation, surface roughness and compressibility of the fluid. Like the classical Reynolds equation, the model is mass preserving. We compute the homogenized coefficients in the case of unidirectional roughness. A one-dimensional problem is also solved explicitly.



Hide All
[1]Almqvist, A., Fabricius, J., Larsson, R. & Wall, P. (2014) A new approach for studying cavitation in lubrication. J. Tribol. 136 (1), 1011706, 6. doi:10.1115/1.4025875
[2]Bayada, G. & Chambat, M. (1986) The transition between the Stokes equation and the Reynolds equation: A mathematical proof. Appl. Math. Optim. 14 (1), 7393.
[3]Bayada, G., Martin, S. & Vásquez, C. (2005) Two-scale homogenization of a hydrodynamic Elrod-Adams model. Asymptot. Anal. 44 (1–2), 75110.
[4]Bayada, G., Martin, S. & Vásquez, C. (2005) An average flow model of the Reynolds roughness including a mass-flow preserving cavitation model. J. Tribol. 127 (4), 793802.
[5]Bensoussan, A., Lions, J. L. & Papanicolaou, G. (1978) Asymptotic Analysis for Periodic Structures, North-Holland Publishing Company, Amsterdam.
[6]Cioranescu, D. & Donato, P. (1999) An Introduction to Homogenization, Oxford University Press, Oxford.
[7]Elrod, H. G. (1981) A cavitation algorithm. J. Tribol. 103 (3), 350354.
[8]Fabricius, J., Koroleva, Y. O. & Wall, P. (2013) A rigorous derivation of the time-dependent Reynolds equation. Asymptot. Anal. 84 (1–2), 103121.
[9]Hamrock, B. J. (1994) Fundamentals of Fluid Film Lubrication, McGraw-Hill, New York.
[10]Lugt, P. M. & Morales-Espejel, G. E. (2011) A review of elasto-hydrodynamic lubrication theory. Tribol. Trans. 54 (3), 470496.
[11]Lukkassen, D., Nguetseng, G. & Wall, P. (2002) Two-scale convergence. Int. J. Pure Appl. Math. 2 (1), 3586.
[12]Lukkassen, D., Meidell, A. & Wall, P. (2011) Analysis of the effects of rough surfaces in compressible thin film flow by homogenization. Int. J. Engrg. Sci. 49 (5), 369377.
[13]Martin, S. (2008) Influence of multiscale roughness patterns in cavitated flows: Applications to journal bearings. Math. Probl. Eng. 2008, 26.
[14]Sahlin, F., Almqvist, A., Larsson, R. & Glavatskih, S. (2007) A cavitation algorithm for arbitrary lubricant compressibility. Tribol. Int. 40 (8), 12941300.
[15]Tsandzana, A. (2014) Homogenization with Applications in Lubrication Theory. Licentiate thesis, Luleå University of Technology.
[16]Tzanakis, I., Hadfield, M., Thomas, B., Noya, S. M., Henshaw, I. & Austen, S. (2012) Future perspectives on sustainable tribology. Renew. Sustainable Energy Rev. 16 (6), 41264140.
[17]Vijayaraghavan, D. & Keith, T. G. Jr (1989) Development and evaluation of a cavitation algorithm. Tribol. Trans. 32 (2), 225233.


Homogenization of a compressible cavitation model



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed