Justification of the Higher Order Effective Model Describing the Lubrication of a Rotating Shaft with Micropolar Fluid
Motivated by the lubrication processes naturally appearing in numerous industrial applications (such as steam turbines, pumps, compressors, motors, etc.), we study the lubrication process of a slipper bearing consisting of two coaxial cylinders in relative motion with an incompressible micropolar fl...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-02-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/12/3/334 |
| _version_ | 1818000457154428928 |
|---|---|
| author | Eduard Marušić–Paloka Igor Pažanin Marko Radulović |
| author_facet | Eduard Marušić–Paloka Igor Pažanin Marko Radulović |
| author_sort | Eduard Marušić–Paloka |
| collection | DOAJ |
| description | Motivated by the lubrication processes naturally appearing in numerous industrial applications (such as steam turbines, pumps, compressors, motors, etc.), we study the lubrication process of a slipper bearing consisting of two coaxial cylinders in relative motion with an incompressible micropolar fluid (lubricant) injected in the thin gap between them. The asymptotic approximation of the solution to the governing micropolar fluid equations is given in the form of a power series in terms of the small parameter <inline-formula> <math display="inline"> <semantics> <mi>ε</mi> </semantics> </math> </inline-formula> representing the thickness of the shaft. The regular part of the approximation is obtained in the explicit form, allowing us to acknowledge the effects of fluid’s microstructure clearly through the presence of the microrotation viscosity in the expressions for the first-order velocity and microrotation correctors. We provide the construction of the boundary layer correctors at the upper and lower boundary of the shaft along with the construction of the divergence corrector, allowing us to improve our overall estimate. The derived effective model is rigorously justified by proving the error estimates, evaluating the difference between the original solution of the considered problem and the constructed asymptotic approximation. |
| first_indexed | 2024-04-14T03:21:57Z |
| format | Article |
| id | doaj.art-88f1afc9494b428a88f75cc885d50f83 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-14T03:21:57Z |
| publishDate | 2020-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-88f1afc9494b428a88f75cc885d50f832022-12-22T02:15:17ZengMDPI AGSymmetry2073-89942020-02-0112333410.3390/sym12030334sym12030334Justification of the Higher Order Effective Model Describing the Lubrication of a Rotating Shaft with Micropolar FluidEduard Marušić–Paloka0Igor Pažanin1Marko Radulović2Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30, 10000 Zagreb, CroatiaDepartment of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30, 10000 Zagreb, CroatiaDepartment of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30, 10000 Zagreb, CroatiaMotivated by the lubrication processes naturally appearing in numerous industrial applications (such as steam turbines, pumps, compressors, motors, etc.), we study the lubrication process of a slipper bearing consisting of two coaxial cylinders in relative motion with an incompressible micropolar fluid (lubricant) injected in the thin gap between them. The asymptotic approximation of the solution to the governing micropolar fluid equations is given in the form of a power series in terms of the small parameter <inline-formula> <math display="inline"> <semantics> <mi>ε</mi> </semantics> </math> </inline-formula> representing the thickness of the shaft. The regular part of the approximation is obtained in the explicit form, allowing us to acknowledge the effects of fluid’s microstructure clearly through the presence of the microrotation viscosity in the expressions for the first-order velocity and microrotation correctors. We provide the construction of the boundary layer correctors at the upper and lower boundary of the shaft along with the construction of the divergence corrector, allowing us to improve our overall estimate. The derived effective model is rigorously justified by proving the error estimates, evaluating the difference between the original solution of the considered problem and the constructed asymptotic approximation.https://www.mdpi.com/2073-8994/12/3/334rotating shaftmicropolar fluidasymptotic analysisrigorous justification |
| spellingShingle | Eduard Marušić–Paloka Igor Pažanin Marko Radulović Justification of the Higher Order Effective Model Describing the Lubrication of a Rotating Shaft with Micropolar Fluid Symmetry rotating shaft micropolar fluid asymptotic analysis rigorous justification |
| title | Justification of the Higher Order Effective Model Describing the Lubrication of a Rotating Shaft with Micropolar Fluid |
| title_full | Justification of the Higher Order Effective Model Describing the Lubrication of a Rotating Shaft with Micropolar Fluid |
| title_fullStr | Justification of the Higher Order Effective Model Describing the Lubrication of a Rotating Shaft with Micropolar Fluid |
| title_full_unstemmed | Justification of the Higher Order Effective Model Describing the Lubrication of a Rotating Shaft with Micropolar Fluid |
| title_short | Justification of the Higher Order Effective Model Describing the Lubrication of a Rotating Shaft with Micropolar Fluid |
| title_sort | justification of the higher order effective model describing the lubrication of a rotating shaft with micropolar fluid |
| topic | rotating shaft micropolar fluid asymptotic analysis rigorous justification |
| url | https://www.mdpi.com/2073-8994/12/3/334 |
| work_keys_str_mv | AT eduardmarusicpaloka justificationofthehigherordereffectivemodeldescribingthelubricationofarotatingshaftwithmicropolarfluid AT igorpazanin justificationofthehigherordereffectivemodeldescribingthelubricationofarotatingshaftwithmicropolarfluid AT markoradulovic justificationofthehigherordereffectivemodeldescribingthelubricationofarotatingshaftwithmicropolarfluid |