| 1. |
- Almqvist, Andreas, et al.
(author)
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Modelling Flows in Lubrication
- 2020. - 1
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In: Modeling and Simulation of Tribological Problems in Technology. - Cham : Springer. ; , s. 229-278
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Book chapter (other academic/artistic)abstract
- This chapter introduces the reader to lubrication theory and describes the governing equations, models and methods that can be used to simulate various types of lubricated systems. It starts with an introduction to the tribological contact and to the different lubrication regimes. The basis for the classical lubrication theory is then given and thereafter follows a presentation of how to obtain the Reynolds equation by means of scaling and asymptotic analysis of the Navier–Stokes equations. After having obtained the Reynolds equation, a quite elaborate presentation of cavitation algorithms is given. It includes discretisation and presents the analytical solution for a pocket bearing as a benchmark model problem. Then, the concept of homogenisation of surface roughness is introduced. This starts from the simplest iso-viscous and incompressible case, expands to include compressibility with a constant bulk modulus constitutive relation and then also addresses the case of ideal gases. Thereafter, the relation between homogenised coefficients and the Patir and Cheng flow factors is described and finally it is shown how to incorporate the effect of mixed lubrication into the model.
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| 2. |
- Kalliorinne, Kalle, et al.
(author)
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Application of topological optimisation methodology to infinitely wide slider bearings operating under compressible flow
- 2020
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In: Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology. - : Sage Publications. - 1350-6501 .- 2041-305X. ; 234:7, s. 1035-1050
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Journal article (peer-reviewed)abstract
- It has been over a century since the interest in inventing the optimal topology for bearings arose. A significant achievement was published by Lord Rayleigh, who found the step-bearing geometry which maximise the load-carrying capacity when the classical Reynolds equation is used to model thin film flow of an iso-viscous and incompressible fluid. Since then, new optimisation methods considering some variants of governing equations for finding the best possible bearings have surfaced, one of which will be presented in this paper. Here, two different formulations for compressible flow, i.e. ideal gas and constant bulk modulus compressibility, as well as the classical Reynolds formulation will be used in combination with the method of moving asymptotes for topological optimisation. All three of these problem formulations provide us with unique geometries, which either maximise the load-carrying capacity or minimise friction, for fluids with a wide variety of compressibility.
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| 3. |
- Pérez-Ràfols, Francesc, 1990-, et al.
(author)
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A Stochastic Two-Scale Model for Rarefied Gas Flow in Highly Heterogeneous Porous Media
- 2020
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In: Transport in Porous Media. - : Springer. - 0169-3913 .- 1573-1634. ; 135:1, s. 219-242
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Journal article (peer-reviewed)abstract
- This paper presents the development of a model enabling the analysis of rarefied gas flow through highly heterogeneous porous media. To capture the characteristics associated with the global- and the local-scale topology of the permeable phase in a typical porous medium, the heterogeneous multi-scale method, which is a flexible framework for constructing two-scale models, was employed. The rapid spatial variations associated with the local-scale topology are accounted for stochastically, by treating the permeability of different local-scale domains as a random variable. The results obtained with the present model show that an increase in the spatial variability in the heterogeneous topology of the porous medium significantly reduces the relevance of rarefaction effects. This clearly shows the necessity of considering a realistic description of the pore topology and questions the applicability of the results obtained for topologies exhibiting regular pore patterns. Although the present model is developed to study low Knudsen number flows, i.e. the slip-flow regime, the same development procedure could be readily adapted for other regimes as well.
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