Numerical study of the Bingham squeeze film problem

O'Donovan, E.J.; Tanner, Roger I.

doi:10.1016/0377-0257(84)80029-4

Cited by 272 publications

(127 citation statements)

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“…The effects of fluid inertia forces and non-Newtonian characteristics of lubricants in the squeeze film bearings have been examined by several investigators, (Tichy and Winer [8], Covey and Stanmore [2], Gartling and Phan-Thien [4], Donovan and Tanner [7], Huang et al [6], Usha and Vimala [9]) but there are few papers attempting to describe the combined effects of fluid inertia forces and non-Newtonian characteristics of lubricants (Elkough [3], Batra and Kandasamy [1]) . Even these works are without considering the sinusoidal motion of the squeeze film bearing.…”

Section: Introductionmentioning

confidence: 99%

Rheodynamic lubrication of a squeeze film bearing under sinusoidal squeeze motion

Kandasamy

Vishwanath

2007

Mat. apl. comput.

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Section: Introductionmentioning

confidence: 99%

Rheodynamic lubrication of a squeeze film bearing under sinusoidal squeeze motion

Kandasamy

Vishwanath

2007

Mat. apl. comput.

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“…An interesting controversy was initiated by Lipscomb and Denn [5] who showed that the unyielded (rigid) zone obtained by using the lubrication approximation for squeeze flow of Bingham materials includes the central plane of the material which however cannot move as a rigid plug for simple kinematic reasons. Gartling and Phan-Thien [6], ODonovan and Tanner [7], and Wilson [8] used instead of the original Bingham model the biviscosity fluid model both for analytical [8] and numerical [6], [7] studies. ODonovan and Tanner [7] solved the squeeze flow problem numerically and showed that unyielded material arises only adjacent to the center of the two disks.…”

Section: Introductionmentioning

confidence: 99%

“…Gartling and Phan-Thien [6], ODonovan and Tanner [7], and Wilson [8] used instead of the original Bingham model the biviscosity fluid model both for analytical [8] and numerical [6], [7] studies. ODonovan and Tanner [7] solved the squeeze flow problem numerically and showed that unyielded material arises only adjacent to the center of the two disks.…”

Section: Introductionmentioning

confidence: 99%

Squeeze Flow of Viscoplastic Bingham Material

Muravleva¹

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. We consider both planar and axisymmetric squeeze flows of a viscoplastic medium. Firstly we deal with no-slip boundary conditions. The asymptotic and the numerical solutions are developed. Previous theoretical analysis of this problem, using the standard lubrication approximation, has led to conflicting results, whereby the material around the plane of symmetry must both behaves as unyielded solid and translates in the main direction with a nonuniform velocity. This variation of the velocity implies that the plug region cannot be truly unyielded. Our solutions show that this region is a pseudo-plug region in which the leading order equation predicts a plug, but really it is weakly yielded at higher order. We follow the asymptotic technique suggested earlier by Balmforth, Craster (1999) and Frigaad, Ryan (2004). The obtained analytical expressions and numerical results are in a very good agreement with the earlier works. For numerical simulations we apply Augmented Lagrangian method (ALM) that yields superior results regarding the location of the yieldsurface. Finite-difference method on staggered grids is used as a discretization technique.Secondly we consider squeeze flow of a Bingham fluid subject to wall slip. If the wall shearstress is smaller than the threshold value (the slip yield stress), the fluid adherence to the boundary is imposed and we have no-slip condition. When the wall shear stress reaches the slip yield stress, the fluid slips along the boundary. We solve numerically this problem also by ALM. The different flow regimes can be observed depending on the relative values of the yield stress and the slip yield stress. More precisely, for the case when the yield stress is smaller than the slip yield stress, there exists a particular value T crit such that when the slip yield stress is greater or equal to T crit ,the material fully sticks at the wall. When the slip yield stress is less than T crit and bigger than the yield stress, the fluid sticks in the central region of the wall and slips close to the outer edges of discsorplates. For the case when the yield stress is bigger than the slip yield stress the material slips on the whole boundary.1215

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“…When considering the biviscous model, as described by O'Donovan and Tanner (1984), stress in the fluid can be described as …”

Section: Continuity Equationmentioning

confidence: 99%