Analysis of Three-Lobe Bearings Having Non-Newtonian Lubricants by a Finite Element Method

1983 ◽  
Vol 7 (1) ◽  
pp. 7-11 ◽  
Author(s):  
D.V. Singh ◽  
R. Sinhasan ◽  
S.P. Tayal
Keyword(s):  
Shear Stress ◽  
Stokes Equations ◽  
Load Capacity ◽  
Navier Stokes ◽  
Shear Strain Rate ◽  
Navier Stokes Equations ◽  
Viscosity Term ◽  
Static Performance ◽  
Iteration Technique ◽  
Element Method

Additives are extensively used in the commercial lubricants to improve their specific qualities. These lubricants are therefore non-Newtonian and their nonlinear relations between shear stress and shear strain rate are generally represented by cubic shear stress laws. The Navier-Stokes equations and the continuity equation in clindrical coordinates, representing the flow-field in the clearance space of each lobe of the three-lobe hydrodynamic journal bearings having Newtonian fluids, are solved by the finie element method using Galerkin’s technique. The solution for non-Newtonian lubricants is obtained by an iteration technique modifying the viscosity term in each iteration. The static performance characteristics have been obtained for both Newtonian and the non-Newtonian lubricants. The load capacity and friction of the bearing decrease with increase in the nonlinearity of the lubricant whereas the end flow is relatively unaffected.

A finite element method for the Navier-Stokes equations in moving domain with application to hemodynamics of the left ventricle

2017 ◽  
Vol 32 (4) ◽  
Author(s):  
Alexander Danilov ◽  
Alexander Lozovskiy ◽  
Maxim Olshanskii ◽  
Yuri Vassilevski
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Left Ventricle ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Computed Tomography Images ◽  
Time Dependent Domain ◽  
Element Method

AbstractThe paper introduces a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method is based on a quasi-Lagrangian formulation of the problem and handling the geometry in a time-explicit way. We prove that numerical solution satisfies a discrete analogue of the fundamental energy estimate. This stability estimate does not require a CFL time-step restriction. The method is further applied to simulation of a flow in a model of the left ventricle of a human heart, where the ventricle wall dynamics is reconstructed from a sequence of contrast enhanced Computed Tomography images.

The turning couples on an elliptic particle settling in a vertical channel

1994 ◽  
Vol 271 ◽  
pp. 1-16 ◽  
Author(s):  
Peter Y. Huang ◽  
Jimmy Feng ◽  
Daniel D. Joseph
Keyword(s):  
Shear Stress ◽  
Vortex Shedding ◽  
Stokes Equations ◽  
Vertical Channel ◽  
Navier Stokes ◽  
Front Face ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Back Face ◽  
The One

We do a direct two-dimensional finite-elment simulation of the Navier–Stokes equations and compute the forces which turn an ellipse settling in a vertical channel of viscous fluid in a regime in which the ellipse oscillates under the action of vortex shedding. Turning this way and that is induced by large and unequal values of negative pressure at the rear separation points which are here identified with the two points on the back face where the shear stress vanishes. The main restoring mechanism which turns the broadside of the ellipse perpendicular to the fall is the high pressure at the ‘stagnation point’ on the front face, as in potential flow, which is here identified with the one point on the front face where the shear stress vanishes.

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