Finite area algorithm for thin film cavitation in openfoam
- 1 Faculty of Mechanical Engineering and Naval Architecture, Zagreb, Croatia
- 2 Luleå University of Technology, Luleå, Sweden
- 3 NV Bekaert SA, Zwevegem, Belgium
Abstract
Numerical algorithm for calculating thin film cavitational effects is presented in this paper. Cavitation is a common phenomenon in diverging parts of thin film contacts, such as: journal bearings, ball bearings, seals, etc. Locating and calculating cavitational effects is very important for their applicability, efficiency and safety. The thin film flow solver based on the Reynolds equation, together with cavitation algorithm is implemented using the Finite Area Method inside the OpenFOAM framework. OpenFOAM is an open source C++ toolbox for computational fluid dynamics (CFD). The Finite Area Method is a two-dimensional counterpart of the Finite Volume Method, used for discretising partial differential equations over curved surfaces. Discretisation is performed on user selected patches of computational mesh, with values calculated at face centres and fluxes calculated at edge centres of each finite area face. Reynolds equation is a 2D partial differential pressure equation used for calculating thin film flows between two surfaces in relative motion, with the following assumptions: fluid viscous forces dominate over body, inertia and surface tensions forces; fluid film curvature can be neglected; variation of pressure across the fluid film is negligibly small. The implemented cavitation algorithm is capable of capturing both rupture and reformation boundaries during cavitation, therefore it is considered to be mass conserving. The implemented solver is validated on three test cases: single parabolic slider (1D), twin parabolic slider (1D) and microtexture pocket bearing (2D).
Keywords
References
- B. J. Hamrock, S. R. Schmid, B. O. Jacobson, Fundamentals of Fluid Film Lubrication (Dekker Mechanical Engineering), CRC Press, 2004.
- H. W. Swift, The Stability of Lubricating Films in Journal Bearings, Minutes of the Proceedings of the Institution of Civil Engineers 233 (1932) (1932) 267-288.
- W. Stieber, Das Schwimmlager: Hydrodynamische Theorie des Gleitlagers, VDI-Verlag, 1933.
- B. Jakobsson, L. Floberg, The finite journal bearing considering vaporization, Transactions of Chalmers University of Technology 190 (1957) 1-116
- K. O. Olsson, Cavitation in dynamically loaded bearings, Transactions of Chalmers University of Technology 308.
- D. Gropper, L. Wang, T. J. Harvey, Hydrodynamic lubrication of textured surfaces: A review of modeling techniques and key findings, Tribology International 94 (2016) 509–529.
- H. Elrod, M. Adams, A Computer Program for Cavitation and Starvation Problems, Cavitation and Related Phenomena in Lubrication 37 (1974) 37-41.
- D. Vijayaraghavan, T. G. Keith, An Efficient, Robust, and Time Accurate Numerical Scheme Applied to a Cavitation Algorithm, Journal of Tribology 112 (1) (1990) 44.
- F. Sahlin, A. Almqvist, R. Larsson, S. Glavatskih, A cavitation algorithm for arbitrary lubricant compressibility, Tribology International 40 (8) (2007) 1294–1300.
- M. Giacopini, M. T. Fowell, D. Dini, A. Strozzi, A MassConserving Complementarity Formulation to Study Lubricant Films in the Presence of Cavitation, Journal of Tribology 132 (4) (2010) 041702.
- L. Bertocchi, D. Dini, M. Giacopini, M. T. Fowell, A. Baldini, Fluid film lubrication in the presence of cavitation: a mass-conserving two-dimensional formulation for compressible, piezoviscous and nonnewtonian fluids, Tribology International 67 (2013) 61– 71.
- A. Almqvist, J. Fabricius, R. Larsson, P. Wall, A New Approach for Studying Cavitation in Lubrication, Journal of Tribology 136 (1) (2013) 011706.
- A. Almqvist, P. Wall, Modelling Cavitation in (Elasto)Hydrodynamic Lubrication, in: Advances in Tribology, Vol. 2, InTech, 2016, p. 64.
- T. Woloszynski, P. Podsiadlo, G. W. Stachowiak, Efficient Solution to the Cavitation Problem in Hydrodynamic Lubrication, Tribology Letters 58 (1).
- F. J. Profito, M. Giacopini, D. C. Zachariadis, D. Dini, A General Finite Volume Method for the Solution of the Reynolds Lubrication Equation with a Mass-Conserving Cavitation Model, Tribology Letters 60 (1).
- G. Bayada, L. Chupin, Compressible fluid model for hydrodynamic lubrication cavitation, Journal of Tribology 135 (4) (2013) 041702.
- D. Dowson, G. R. Higginson, Elasto-Hydrodynamic Lubrication: International Series on Materials Science and Technology, Pergamon, 2014.
- K. L. Johnson, J. L. Tevaarwerk, Shear behaviour of elastohydrodynamic oil films, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 356 (1685) (1977) 215–236.
- Ž. Tuković, Metoda kontrolnih volumena na domenama promjenjivog oblika, Ph.D. thesis in Croatian, Chair of Turbomachinery, Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb (2005).