Open this publication in new window or tab >>2023 (English)In: Applications in Engineering Science, ISSN 2666-4968, Vol. 15, article id 100145Article in journal (Refereed) Published
Abstract [en]
Flows of incompressible NavierâStokes (Newtonian) fluids between adjacent surfaces are encountered in numerous practical applications, such as seal leakage and bearing lubrication. In seals, the flow is primarily pressure-driven, whereas, in bearings, the dominating driving force is due to shear. The governing NavierâStokes system of equations can be significantly simplified due to the small distance between the surfaces compared to their size. From the simplified system, it is possible to derive a single lower-dimensional equation, known as the Reynolds equation, which describes the pressure field. Once the pressure field is computed, it can be used to determine the velocity field. This computational algorithm is much simpler to implement than a direct numerical solution of the NavierâStokes equations and is therefore widely employed by engineers. The primary objective of this article is to investigate the possibility of deriving a type of Reynolds equation also for non-Newtonian fluids, using the balance of linear momentum. By considering power-law fluids we demonstrate that it is not possible for shear-driven flows, whereas it is feasible for pressure-driven flows. Additionally, we demonstrate that in the full 3D model, a normal stress boundary condition at the inlet/outlet implies a Dirichlet condition for the pressure in the Reynolds equation associated with pressure-driven flow. Furthermore, we establish that a Dirichlet condition for the velocity at the inlet/outlet in the 3D model results in a Neumann condition for the pressure in the Reynolds equation.
Place, publisher, year, edition, pages
Elsevier, 2023
Keywords
Navier-Stokes equation, Reynolds equation, Poiseuille law, Lower-dimensional model, Power-law fluid, Non-Newtonian fluid
National Category
Mathematical Analysis
Research subject
Machine Elements; Applied Mathematics
Identifiers
urn:nbn:se:ltu:diva-102664 (URN)10.1016/j.apples.2023.100145 (DOI)001080276800001 ()2-s2.0-85169543467 (Scopus ID)
Funder
Swedish Research Council, DNR 2019-04293
Note
Validerad;2023;Nivå 2;2023-11-21 (joosat);
CC BY-NC-ND 4.0 License;
2023-11-212023-11-212024-11-20Bibliographically approved