TY - JOUR
T1 - Efficient solution method for the Reynolds equation with Herschel–Bulkley fluids
AU - van der Meer, G. H.G.
AU - van Ostayen, R. A.J.
PY - 2025
Y1 - 2025
N2 - Thin film lubrication problems frequently involve the use of lubricants with non-Newtonian characteristics, and a relatively simple viscosity model that can describe several non-Newtonian fluids is the Herschel–Bulkley relation. This relation can model solid-like properties of a lubricant at low shear stress using a yield stress, while at higher shear stress values shear-thinning or thickening can be included. In literature, this viscosity model has been combined with various governing equations to solve the non-Newtonian thin film problem, resulting in models that range from full 3D CFD simulations, to 1D Reynolds equation based methods. However, something that all of these approaches have in common is that they are either computationally expensive, can only be used for 1D geometries, or use non-exact, regularised versions of the Herschel–Bulkley model for reasons of numerical stability. This paper therefore introduces a method for solving a thin film problem with a non-regularised Herschel–Bulkley lubricant using the 2D generalised Reynolds equation, and this approach is shown to be fast without compromising on accuracy. The increased speed will allow the model to be used more efficiently in complex simulations or design optimisation scenarios.
AB - Thin film lubrication problems frequently involve the use of lubricants with non-Newtonian characteristics, and a relatively simple viscosity model that can describe several non-Newtonian fluids is the Herschel–Bulkley relation. This relation can model solid-like properties of a lubricant at low shear stress using a yield stress, while at higher shear stress values shear-thinning or thickening can be included. In literature, this viscosity model has been combined with various governing equations to solve the non-Newtonian thin film problem, resulting in models that range from full 3D CFD simulations, to 1D Reynolds equation based methods. However, something that all of these approaches have in common is that they are either computationally expensive, can only be used for 1D geometries, or use non-exact, regularised versions of the Herschel–Bulkley model for reasons of numerical stability. This paper therefore introduces a method for solving a thin film problem with a non-regularised Herschel–Bulkley lubricant using the 2D generalised Reynolds equation, and this approach is shown to be fast without compromising on accuracy. The increased speed will allow the model to be used more efficiently in complex simulations or design optimisation scenarios.
KW - Finite element method
KW - Generalised Reynolds equation
KW - Journal bearing
KW - Non-Newtonian fluids
UR - http://www.scopus.com/inward/record.url?scp=85212215130&partnerID=8YFLogxK
U2 - 10.1016/j.triboint.2024.110460
DO - 10.1016/j.triboint.2024.110460
M3 - Article
AN - SCOPUS:85212215130
SN - 0301-679X
VL - 204
JO - Tribology International
JF - Tribology International
M1 - 110460
ER -