| 1. |
- Almqvist, Andreas, et al.
(författare)
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A new approach for studying cavitation in lubrication
- 2014
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Ingår i: Journal of tribology. - : ASME International. - 0742-4787 .- 1528-8897. ; 136:1
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Tidskriftsartikel (refereegranskat)abstract
- The underlying theory, in this paper, is based on clear physical arguments related to conservation of mass flow and considers both incompressible and compressible fluids. The result of the mathematical modeling is a system of equations with two unknowns, which are related to the hydrodynamic pressure and the degree of saturation of the fluid. Discretization of the system leads to a linear complementarity problem (LCP), which easily can be solved numerically with readily available standard methods and an implementation of a model problem in matlab code is made available for the reader of the paper. The model and the associated numerical solution method have significant advantages over today's most frequently used cavitation algorithms, which are based on Elrod-Adams pioneering work
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| 2. |
- Almqvist, Andreas, et al.
(författare)
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Flow in thin domains with a microstructure : Lubrication and thin porous media
- 2017
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Ingår i: AIP Conference Proceedings. - : AIP Publishing. - 0094-243X .- 1551-7616. ; 1798
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Tidskriftsartikel (refereegranskat)abstract
- This paper is devoted to homogenization of different models of flow in thin domains with a microstructure. The focus is on applications connected to the effect of surface roughness in full film lubrication, but a parallel to flow in thin porous media is also discussed. Mathematical models of such flows naturally include two small parameters. One is connected to the fluid film thickness and the other to the microstructure. The corresponding asymptotic analysis is a delicate problem, since the result depends on how fast the two small parameters tend to zero relative to each other. We give a review of the current status in this area and point out some future challenges.
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| 3. |
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| 4. |
- Almqvist, Andreas, et al.
(författare)
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Homogenization of a Reynolds equation describing compressible flow
- 2012
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Ingår i: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X .- 1096-0813. ; 390:2, s. 456-471
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Tidskriftsartikel (refereegranskat)abstract
- We homogenize a Reynolds equation with rapidly oscillating film thickness function hε, assuming a constant compressiblity factor in the pressure-density relation. The oscillations are due to roughness on the bounding surfaces of the fluid film. As shown by previous studies, homogenization is an effective approach for analyzing the effects of surface roughness in hydrodynamic lubrication. By two-scale convergence theory we obtain the limit problem (homogenized equation) and strong convergence in L2 for the unknown density ρε. By adding a small corrector term we also obtain strong convergence in the Sobolev norm.
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| 5. |
- Almqvist, Andreas, et al.
(författare)
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Multiscale homogenization of a class of nonlinear equations with applications in lubrication theory and applications
- 2011
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Ingår i: Journal of Function Spaces and Applications. - : Hindawi Limited. - 0972-6802 .- 1758-4965. ; 9:1, s. 17-40
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Tidskriftsartikel (refereegranskat)abstract
- We prove a homogenization result for monotone operators by using the method of multiscale convergence. More precisely, we study the asymptotic behavior as epsilon -> 0 of the solutions u(epsilon) of the nonlinear equation div a(epsilon)(x, del u(epsilon)) = div b(epsilon), where both a(epsilon) and b(epsilon) oscillate rapidly on several microscopic scales and a(epsilon) satisfies certain continuity, monotonicity and boundedness conditions. This kind of problem has applications in hydrodynamic thin film lubrication where the bounding surfaces have roughness on several length scales. The homogenization result is obtained by extending the multiscale convergence method to the setting of Sobolev spaces W-0(1,p)(Omega), where 1 < p < infinity. In particular we give new proofs of some fundamental theorems concerning this convergence that were first obtained by Allaire and Briane for the case p = 2.
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| 6. |
- Almqvist, Andreas, et al.
(författare)
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Reiterated homogenization applied in hydrodynamic lubrication
- 2008
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Ingår i: Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology. - 1350-6501 .- 2041-305X. ; 222:7, s. 827-841
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Tidskriftsartikel (refereegranskat)abstract
- This work is devoted to studying the combined effect that arises due to surface texture and surface roughness in hydrodynamic lubrication. An effective approach in tackling this problem is by using the theory of reiterated homogenization with three scales. In the numerical analysis of such problems, a very fine mesh is needed, suggesting some type of averaging. To this end, a general class of problems is studied that, e.g. includes the incompressible Reynolds problem in both artesian and cylindrical coordinate forms. To demonstrate the effectiveness of the method several numerical results are presented that clearly show the convergence of the deterministic solutions towards the homogenized solution.Moreover, the convergence of the friction force and the load carrying capacity of the lubricant film is also addressed in this paper. In conclusion, reiterated homogenization is a feasible mathematical tool that facilitates the analysis of this type of problem.
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| 7. |
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| 8. |
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| 9. |
- Almqvist, Andreas, et al.
(författare)
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Similarities and differences between the flow factor method by Patir and Cheng and homogenization
- 2011
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Ingår i: Journal of tribology. - : ASME International. - 0742-4787 .- 1528-8897. ; 133:3, s. 031702-1
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Tidskriftsartikel (refereegranskat)abstract
- Different averaging techniques have proved to be useful for analyzing the effects of surface roughness in hydrodynamic lubrication. This paper compares two of these averaging techniques, namely the flow factor method by Patir and Cheng (P&C) and homogenization. It has been rigorously proved by many authors that the homogenization method provides a correct solution for arbitrary roughness. In this work it is shown that the two methods coincide if and only if the roughness exhibits certain symmetries. Hence, homogenization is always the preferred method.
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| 10. |
- Almqvist, Andreas, et al.
(författare)
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Variational bounds applied to unstationary hydrodynamic lubrication
- 2008
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Ingår i: International Journal of Engineering Science. - : Elsevier BV. - 0020-7225 .- 1879-2197. ; 46:9, s. 891-906
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Tidskriftsartikel (refereegranskat)abstract
- This paper is devoted to the effects of surface roughness in hydrodynamic lubrication. The numerical analysis of such problems requires a very fine mesh to resolve the surface roughness, hence it is often necessary to do some type of averaging. Previously, homogenization (a rigorous form of averaging) has been successfully applied to Reynolds type differential equations. More recently, the idea of finding upper and lower bounds on the effective behavior, obtained by homogenization, was applied for the first time in tribology. In these pioneering works, it has been assumed that only one surface is rough. In this paper we develop these results to include the unstationary case where both surfaces may be rough. More precisely, we first use multiple-scale expansion to obtain a homogenization result for a class of variational problems including the variational formulation associated with the unstationary Reynolds equation. Thereafter, we derive lower and upper bounds corresponding to the homogenized (averaged) variational problem. The bounds reduce the numerical analysis, in that one only needs to solve two smooth problems, i.e. no local scale has to be considered. Finally, we present several examples, where it is shown that the bounds can be used to estimate the effects of surface roughness with very high accuracy.
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