scholarly journals Experimental Determination of Limit Adhesive Shear Stress between Solid Wall and Liquid

2014 ◽  
Vol 61 (3-4) ◽  
pp. 175-181
Author(s):  
Jerzy M. Sawicki
Keyword(s):  
Boundary Condition ◽  
Shear Stress ◽  
Theoretical Analysis ◽  
Solid Wall ◽  
Slip Boundary Condition ◽  
Low Velocity ◽  
Slip Boundary ◽  
Gravitational Forces ◽  
Limit Value

AbstractThe slip boundary condition can be a very useful relation when some specific problems of hydromechanics are considered. According to the classical form of this condition, the slip of a fluid with respect to the solid wall should occur even at a very low velocity of motion. However, both theoretical analysis and certain empirical data suggest that there must be a limit value of the wall shear stress, below which the slip does not occur. According to the simplified balance of adhesive and gravitational forces, a simple experimental method for determining this stress has been proposed and applied in this paper.

MEMS-Scale Turbomachinery Based Vacuum Roughing Pump

2014 ◽  
Vol 136 (10) ◽  
Author(s):  
Anthony J. Gannon ◽  
Garth V. Hobson ◽  
Michael J. Shea ◽  
Christopher S. Clay ◽  
Knox T. Millsaps
Keyword(s):  
Boundary Condition ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Boundary Conditions ◽  
Knudsen Number ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
3D Simulations ◽  
Slip Boundary ◽  
Wall Shear

This study forms part of a program to develop a micro-electro-mechanical systems (MEMS) scale turbomachinery based vacuum pump and investigates the roughing portion of such a system. Such a machine would have many radial stages with the exhaust stages operating near atmospheric conditions while the inlet stages operate at near vacuum conditions. In low vacuum such as those to the inlet of a roughing pump, the flow can still be treated as a continuum; however, the no-slip boundary condition is not accurate. The Knudsen number becomes a dominant nondimensional parameter in these machines due to their small size and low pressures. As the Knudsen number increases, slip-flow becomes present at the walls. The study begins with a basic overview on implementing the slip wall boundary condition in a commercial code by specifying the wall shear stress based on the mean-free-path of the gas molecules. This is validated against an available micro-Poiseuille classical solution at Knudsen numbers between 0.001 and 0.1 with reasonable agreement found. The method of specifying the wall shear stress is then applied to a generic MEMS scale roughing pump stage that consists of two stators and a rotor operating at a nominal absolute pressure of 500 Pa. The zero flow case was simulated in all cases as the pump down time for these machines is small due to the small volume being evacuated. Initial transient two-dimensional (2D) simulations are used to evaluate three boundary conditions, classical no-slip, specified-shear, and slip-flow. It is found that the stage pressure rise increased as the flow began to slip at the walls. In addition, it was found that at lower pressures the pure slip boundary condition resulted in very similar predictions to the specified-shear simulations. As the specified-shear simulations are computationally expensive it is reasonable to use slip-flow boundary conditions. This approach was used to perform three-dimensional (3D) simulations of the stage. Again the stage pressure increased when slip-flow was present compared with the classical no-slip boundaries. A characteristic of MEMS scale turbomachinery are the large relative tip gaps requiring 3D simulations. A tip gap sensitivity study was performed and it was found that when no-slip boundaries were present the pressure ratio increased significantly with decreasing tip gap. When slip-flow boundaries were present, this relationship was far weaker.

Numerical Simulation of Newtonian Fluid Flow in a T-Channel with no Slip/Slip Boundary Conditions on a Solid Wall

2017 ◽  
Vol 743 ◽  
pp. 480-485
Author(s):  
Evgeny Borzenko ◽  
Olga Dyakova
Keyword(s):  
Boundary Condition ◽  
Fluid Flow ◽  
Solid Wall ◽  
Simple Procedure ◽  
Slip Boundary Condition ◽  
Navier Slip ◽  
Slip Boundary ◽  
Pressure Profiles ◽  
Slip Yield Stress ◽  
Solid Walls

The planar flow of a Newtonian incompressible fluid in a T-shaped channel is investigated. Three fluid interaction models with solid walls are considered: no slip boundary condition, Navier slip boundary condition and slip boundary condition with slip yield stress. The fluid flow is provided by uniform pressure profiles at the boundary sections of the channel. The problem is numerically solved using a finite difference method based on the SIMPLE procedure. Characteristic flow regimes have been found for the described models of liquid interaction with solid walls. The estimation of the influence of the Reynolds number, pressure applied to the boundary sections and the parameters of these models on the flow pattern was performed. The criterial dependences describing main characteristics of the flow under conditions of the present work have been demonstrated.

scholarly journals On the dynamic slip boundary condition for Navier–Stokes-like problems

2021 ◽  
pp. 1-48
Author(s):  
Anna Abbatiello ◽  
Miroslav Bulíček ◽  
Erika Maringová
Keyword(s):  
Boundary Condition ◽  
Shear Stress ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Slip Boundary ◽  
Boundary Terms ◽  
The Moment ◽  
Dynamic Slip ◽  
Proper Generalization ◽  
Slip Phenomenon

The choice of the boundary conditions in mechanical problems has to reflect the interaction of the considered material with the surface. Still the assumption of the no-slip condition is preferred in order to avoid boundary terms in the analysis and slipping effects are usually overlooked. Besides the “static slip models”, there are phenomena that are not accurately described by them, e.g. at the moment when the slip changes rapidly, the wall shear stress and the slip can exhibit a sudden overshoot and subsequent relaxation. When these effects become significant, the so-called dynamic slip phenomenon occurs. We develop a mathematical analysis of Navier–Stokes-like problems with a dynamic slip boundary condition, which requires a proper generalization of the Gelfand triplet and the corresponding function space setting.

Incompressible slip flow past a semi-infinite flat plate

1965 ◽  
Vol 22 (3) ◽  
pp. 463-469 ◽  
Author(s):  
J. D. Murray
Keyword(s):  
Boundary Condition ◽  
Shear Stress ◽  
Viscous Fluid ◽  
Flat Plate ◽  
Slip Velocity ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Slip Boundary

An asymptotic solution to the Navier-Stokes equation is obtained for the incompressible flow of a viscous fluid past a semi-infinite flat plate when a slip boundary condition is applied at the plate. The results for the shear stress (and hence the slip velocity) on the plate differ basically from those obtained by previous authors who considered the same problem using some form of the Oseen equations.

MEMS-Scale Turbomachinery Based Vacuum Roughing Pump

2013 ◽  
Author(s):  
Anthony J. Gannon ◽  
Garth V. Hobson ◽  
Michael J. Shea ◽  
Christopher S. Clay ◽  
Knox T. Millsaps
Keyword(s):  
Boundary Condition ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Boundary Conditions ◽  
Knudsen Number ◽  
Slip Flow ◽  
Three Dimensional ◽  
Slip Boundary Condition ◽  
Slip Boundary ◽  
Three Dimensional Simulations

This study forms part of a program to develop a micro-electro-mechanical-systems (MEMS) scale turbomachinery based vacuum pump and investigates the roughing portion of such a system. Such a machine would have many radial stages with the exhaust stages operating near atmospheric conditions while the inlet stages operate at near vacuum conditions. In low vacuum such as those to the inlet of a roughing pump the flow can still be treated as a continuum however the no-slip boundary condition is not accurate. The Knudsen number becomes a dominant non-dimensional parameter in these machines due to their small size and low pressures. As the Knudsen number increases slip flow becomes present at the walls. The study begins with a basic overview on implementing the slip wall boundary condition in a commercial code by specifying the wall shear stress based on the mean-free-path of the gas molecules. This is validated against an available micro-Poiseuille classical solution at Knudsen numbers between 0.001–0.1 with reasonable agreement found. The method of specifying the wall-shear stress is then applied to a generic MEMS scale roughing pump stage that consists of two stators and a rotor operating at a nominal absolute pressure of 500 Pa. The zero flow case was simulated in all cases as the pump down time for these machines is small due to the small volume being evacuated. Initial transient two-dimensional simulations are used to evaluate three boundary conditions, classical no-slip, specified-shear and slip-flow. It is found that the stage pressure rise increased as the flow began to slip at the walls. In addition it was found that at lower pressures the pure slip boundary condition resulted in very similar predictions to the specified shear simulations. As the specified-shear simulations are computationally expensive it is reasonable to use slip-flow boundary conditions. This approach was used to perform three-dimensional simulations of the stage. Again the stage pressure increased when slip-flow was present compared with the classical no-slip boundaries. A characteristic of MEMS scale turbomachinery are the large relative tip gaps requiring three-dimensional simulations. A tip gap sensitivity study was performed and it was found that when no-slip boundaries were present the pressure ratio increased significantly with decreasing tip gap. When slip-flow boundaries were present this relationship was far weaker.

NO-SLIP BOUNDARY CONDITION IN DISSIPATIVE PARTICLE DYNAMICS

2000 ◽  
Vol 11 (05) ◽  
pp. 881-890 ◽  
Author(s):  
S. M. WILLEMSEN ◽  
H. C. J. HOEFSLOOT ◽  
P. D. IEDEMA
Keyword(s):  
Boundary Condition ◽  
Solid Wall ◽  
Dissipative Particle Dynamics ◽  
Slip Boundary Condition ◽  
Particle Dynamics ◽  
Particle Methods ◽  
Driven Cavity ◽  
Slip Boundary ◽  
Computational Fluid Dynamics Cfd ◽  
Solid Walls

Dissipative Particle Dynamics (DPD) has, with only a few exceptions, been used to study hydrodynamic behavior of complex fluids without confinement. Previous studies used a periodic boundary condition, and only bulk behavior can be studied effectively. However, if solid walls play an important role in the problem to be studied, a no-slip boundary condition in DPD is required. Until now the methods used to impose a solid wall consisted of a frozen layer of particles. If the wall density is equal to the density of the simulated domain, slip phenomena are observed. To suppress this slip, the density of the wall has to be increased. We introduce a new method, which intrinsically imposes the no-slip boundary condition without the need to artificially increase the density in the wall. The method is tested in both a steady-state and an instationary calculation. If repulsion is applied in frozen particle methods, density distortions are observed. We propose a method to avoid these distortions. Finally, this method is tested against conventional computational fluid dynamics (CFD) calculations for the flow in a lid-driven cavity. Excellent agreement between the two methods is found.

scholarly journals Theoretical Analysis of the No-Slip Boundary Condition Enforcement in SPH Methods

2011 ◽  
Vol 125 (6) ◽  
pp. 1091-1121 ◽  
Author(s):  
F. Macia ◽  
M. Antuono ◽  
L. M. Gonzalez ◽  
A. Colagrossi
Keyword(s):  
Boundary Condition ◽  
Theoretical Analysis ◽  
Slip Boundary Condition ◽  
Slip Boundary
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