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.

Numerical investigation of flow around a structure using Navier-slip boundary conditions

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Sang-Do Choi ◽  
Tae-Soo Eum ◽  
Eun Taek Shin ◽  
Chang Geun Song
Keyword(s):  
Boundary Conditions ◽  
Slip Length ◽  
Lift Coefficient ◽  
Vortex Formation ◽  
Slip Condition ◽  
Partial Slip ◽  
Slip Boundary Conditions ◽  
Content Type ◽  
Navier Slip ◽  
Slip Boundary

Purpose Complicated motion of vortex is frequently observed in the wake of islands. These kinds of swirling fluid cause the trap of sediments or pollutants, subsequently inducing the dead zone, odor or poor water quality. Therefore, the understanding of flow past a circular cylinder is significant in predicting water quality and positioning the immersed structures. This study aims to investigate the flow properties around a structure using Navier-slip boundary conditions. Design/methodology/approach Boundary conditions are a major factor affecting the flow pattern because the magnitude of flow detachment on a surface can redistribute the tangential stress on the wall. Therefore, the authors performed an analysis of laminar flow passing through a circular structure to investigate the effect of boundary conditions on the flow pattern. Findings The authors examined the relationship between the partial-slip boundary conditions and the flow behavior at low Reynolds number past a circular cylinder considering velocity and vorticity distributions behind the cylinder, lift coefficient and Strouhal number. The amplitude of lift coefficient by the partial slip condition had relatively small value compared with that of no-slip condition, as the wall shear stress acting on the cylinder became smaller by the velocity along the cylinder surface. The frequency of the asymmetrical vortex formation with partial slip velocity was increased compared with no-slip case due to the intrinsic inertial effect of Navier-slip condition. Originality/value The ability to engineer slip could have dramatic influences on flow, as the viscous dominated motion can lead to large pressure drops and large axial dispersion. By the slip length control, no-slip, partial-slip and free-slip boundary conditions are tunable, and the velocity distributions at the wall, vortex formation and wake pattern including the amplitude of lift coefficient and frequency were significantly affected by slip length parameter.

scholarly journals DYNAMICS OF PULSATILE FLOWS THROUGH ELASTIC MICROTUBES

2012 ◽  
Vol 04 (01) ◽  
pp. 1250006 ◽  
Author(s):  
OMER SAN ◽  
ANNE E. STAPLES
Keyword(s):  
Boundary Conditions ◽  
Slip Length ◽  
Small Deformation ◽  
Elastic Behavior ◽  
Slip Boundary Conditions ◽  
Slip Ratio ◽  
Transient Flows ◽  
Navier Slip ◽  
Slip Boundary ◽  
Navier Slip Boundary Conditions

We investigate the dynamics of pressure driven-transient flows of incompressible Newtonian fluids through circular microtubes having thin elastic walls under the long-wavelength and small deformation assumptions, which are valid for many industrial and biological processes. An analytical solution of the coupled fluid and solid equations is found using Navier slip boundary conditions and is shown to include some existing Womersley solutions as limiting cases. The effect of the slip length at the fluid–solid interface is analyzed for oscillatory pressure gradients using a range of slip ratio and frequency parameters. The solutions for elastic and rigid walls are compared for the cases with and without slip boundary conditions for a broad range of the relevant parameters. It is shown that the elastic behavior of the microtube couples nonlinearly with the slip velocity, which greatly enhances the achievable flow rate and pumping efficacy compared to the inelastic case. In addition, it is observed that increasing the slip length produces less shear stress, which is consistent with the nearly frictionless interfaces observed in many microscale experiments.

scholarly journals Asymptotic analysis of an optimal control problem for a viscous incompressible fluid with Navier slip boundary conditions

2021 ◽  
pp. 1-21
Author(s):  
Claudia Gariboldi ◽  
Takéo Takahashi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Boundary Conditions ◽  
Control Problem ◽  
Stokes System ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Slip ◽  
Slip Boundary ◽  
Navier Slip Boundary Conditions

We consider an optimal control problem for the Navier–Stokes system with Navier slip boundary conditions. We denote by α the friction coefficient and we analyze the asymptotic behavior of such a problem as α → ∞. More precisely, we prove that if we take an optimal control for each α, then there exists a sequence of optimal controls converging to an optimal control of the same optimal control problem for the Navier–Stokes system with the Dirichlet boundary condition. We also show the convergence of the corresponding direct and adjoint states.

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.

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