Numerical Solution of Reynolds Equation With Slip Boundary Conditions for Cases of Large Bearing Number (Λ > 300)

1979 ◽  
Vol 101 (1) ◽  
pp. 64-66 ◽  
Author(s):  
A. Sereny ◽  
V. Castelli
Keyword(s):  
Boundary Layer ◽  
Boundary Conditions ◽  
Exact Solutions ◽  
Numerical Solution ◽  
Reynolds Equation ◽  
Slip Boundary Conditions ◽  
Grid Spacing ◽  
Slip Boundary ◽  
Finite Differencing ◽  
Bearing Number

The behavior of two numerical discretizations for the solution of Reynolds equation with slip boundary conditions for cases of large bearing number is described. The narrow boundary layer caused by the large bearing number is well handled by a variable grid spacing. The performance of these methods is compared against exact solutions for the ∞-wide case. It is clearly demonstrated that discretization which satisfies integral conservation is preferable to the differential procedure of finite differencing.

Perturbation Solution of the 1-D Reynolds Equation With Slip Boundary Conditions

1978 ◽  
Vol 100 (1) ◽  
pp. 70-73 ◽  
Author(s):  
Aron Sereny ◽  
Vittorio Castelli
Keyword(s):  
Boundary Conditions ◽  
Numerical Solution ◽  
Carrying Capacity ◽  
Reynolds Equation ◽  
Load Carrying Capacity ◽  
Slip Boundary Conditions ◽  
Slider Bearing ◽  
Slip Boundary ◽  
Load Carrying ◽  
Bearing Number

The method of matched asymptotic expansion is applied to obtain the pressure distribution and the load carrying capacity for an infinitely long slider bearing, operating under high-speed, low-height, with slip boundary conditions. The pressure distribution is easily applicable as the starting solution for the iterative numerical solution of Reynolds equation. Two examples given show extremely good correlation between this expansion and the numerical solution. It is shown that, for a tapered slider bearing with a bearing number above 100, the reduction in load because of slip is minimal and that, for a parabolic slider, there exists a certain unique bearing number for which the load carrying capacity is independent of the parabolic crown of the slider. It is shown that for a wide slider bearing with large bearing number, the effect of slip is on the order of 1/A.

scholarly journals Suction/Injection Effects on the Swirling Flow of a Reiner-Rivlin Fluid near a Rough Surface

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Bikash Sahoo ◽  
Sébastien Poncet ◽  
Fotini Labropulu
Keyword(s):  
Boundary Layer ◽  
Boundary Conditions ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Swirling Flow ◽  
Velocity Profiles ◽  
Partial Slip ◽  
Injection Velocity ◽  
Slip Boundary Conditions ◽  
Slip Boundary

The similarity equations for the Bödewadt flow of a non-Newtonian Reiner-Rivlin fluid, subject to uniform suction/injection, are solved numerically. The conventional no-slip boundary conditions are replaced by corresponding partial slip boundary conditions, owing to the roughness of the infinite stationary disk. The combined effects of surface slip (λ), suction/injection velocity (W), and cross-viscous parameter (L) on the momentum boundary layer are studied in detail. It is interesting to find that suction dominates the oscillations in the velocity profiles and decreases the boundary layer thickness significantly. On the other hand, injection has opposite effects on the velocity profiles and the boundary layer thickness.

scholarly journals Stability Analysis on Nonequilibrium Supersonic Boundary Layer Flow with Velocity-Slip Boundary Conditions

Fluids ◽  
2019 ◽  
Vol 4 (3) ◽  
pp. 142
Author(s):  
Xin He ◽  
Kai Zhang ◽  
Chunpei Cai
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Boundary Conditions ◽  
Boundary Layer Flow ◽  
Velocity Slip ◽  
Linear Stability Theory ◽  
Resonance Phenomenon ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Layer Flow

This paper presents our recent work on investigating velocity slip boundary conditions’ effects on supersonic flat plate boundary layer flow stability. The velocity-slip boundary conditions are adopted and the flow properties are obtained by solving boundary layer equations. Stability analysis of two such boundary layer flows is performed by using the Linear stability theory. A global method is first utilized to obtain approximate discrete mode values. A local method is then utilized to refine these mode values. All the modes in these two scenarios have been tracked upstream-wisely towards the leading edge and also downstream-wisely. The mode values for the no-slip flows agree well with the corresponding past results in the literature. For flows with slip boundary conditions, a stable and an unstable modes are detected. Mode tracking work is performed and the results illustrate that the resonance phenomenon between the stable and unstable modes is delayed with slip boundary conditions. The enforcement of the slip boundary conditions also shortens the unstable mode region. As to the conventional second mode, flows with slip boundary conditions can be more stable streamwisely when compared with the results for corresponding nonslip flows.

scholarly journals Researches Concerning the Lubrication of Profiled Surfaces in Slip Boundary Conditions

2020 ◽  
Vol 12 (4) ◽  
pp. 163-172
Author(s):  
Alexandru Valentin RADULESCU ◽  
Irina RADULESCU
Keyword(s):  
Boundary Conditions ◽  
Pressure Distribution ◽  
Reynolds Equation ◽  
Lower Surface ◽  
Newtonian Fluids ◽  
Squeeze Film ◽  
Loading Capacity ◽  
Slip Boundary Conditions ◽  
Slip Boundary

The paper investigates the squeeze film process for non-Newtonian fluids between two circular parallel profiled surfaces. The lower surface is characterized by the existence of a cylindrical or spherical dimple in the center, which is specific for profiled surfaces by texturing. In order to integrate the Reynolds equation, the slip boundary conditions on the upper surface have been assumed. Finally, the pressure distribution and the loading capacity of the non-Newtonian film are obtained.

scholarly journals Solution of Time Periodic Electroosmosis Flow with Slip Boundary

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Qian Sun ◽  
Yonghong Wu ◽  
Lishan Liu ◽  
B. Wiwatanapataphee
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Solid Surface ◽  
Electroosmotic Flow ◽  
Mixing Enhancement ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Flow Problems ◽  
Micrometer Scale ◽  
Time Periodic

Recent research confirms that slip of a fluid on the solid surface occurs at micrometer scale. Slip on solid surface may cause the change of interior material deformation which consequently leads to the change of velocity profile and stress field. This paper concerns the time periodic electroosmotic flow in a channel with slip boundary driven by an alternating electric field, which arises from the study of particle manipulation and separation such as flow pumping and mixing enhancement. Although exact solutions to various flow problems of electroosmotic flows under the no-slip condition have been obtained, exact solutions for problems under slip boundary conditions have seldom been addressed. In this paper, an exact solution is derived for the time periodic electroosmotic flow in two-dimensional straight channels under slip boundary conditions.

scholarly journals Dynamics of a small gap gas lubricated bearing with Navier slip boundary conditions

2017 ◽  
Vol 818 ◽  
pp. 68-99 ◽  
Author(s):  
N. Y. Bailey ◽  
S. Hibberd ◽  
H. Power
Keyword(s):  
Boundary Conditions ◽  
Reynolds Equation ◽  
Slip Length ◽  
Velocity Slip ◽  
Structural Equations ◽  
Force Balance ◽  
Slip Boundary Conditions ◽  
Inertia Effects ◽  
Navier Slip ◽  
Slip Boundary

A gas lubricated bearing model is derived which is appropriate for a very small bearing face separation by including velocity slip boundary conditions and centrifugal inertia effects. The bearing dynamics is examined when an external harmonic force is imposed on the bearing due to the bearing being situated within a larger complex dynamical system. A compressible Reynolds equation is formulated for the gas film which is coupled to the bearing structure through an axial force balance where the rotor and stator correspond to spring–mass–damper systems. Surface slip boundary conditions are derived on the bearing faces, characterised by the slip length parameter. The coupled bearing system is analysed using a stroboscopic map solver with the modified Reynolds equation and structural equations solved simultaneously. For a sufficiently large forcing amplitude a flapping motion of the bearing faces is induced when the rotor and stator are in close proximity. The minimum bearing gap over the time period of the external forcing is examined for a range of bearing parameters.

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