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.

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.

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.

NEW MODELS IN MICROPOLAR FLUID AND THEIR APPLICATION TO LUBRICATION

2005 ◽  
Vol 15 (03) ◽  
pp. 343-374 ◽  
Author(s):  
GUY BAYADA ◽  
NADIA BENHABOUCHA ◽  
MICHÈLE CHAMBAT
Keyword(s):  
Boundary Condition ◽  
Friction Coefficient ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Micropolar Fluid ◽  
Reynolds Equation ◽  
Slip Boundary Condition ◽  
Slip Boundary ◽  
New Models ◽  
Uniqueness Of The Solution

A thin micropolar fluid with new boundary conditions at the fluid-solid interface, linking the velocity and the microrotation by introducing a so-called "boundary viscosity" is presented. The existence and uniqueness of the solution is proved and, by way of asymptotic analysis, a generalized micropolar Reynolds equation is derived. Numerical results show the influence of the new boundary conditions for the load and the friction coefficient. Comparisons are made with other works retaining a no slip boundary condition.

scholarly journals Experimental study of wall boundary conditions for large-eddy simulation

2001 ◽  
Vol 446 ◽  
pp. 309-320 ◽  
Author(s):  
IVAN MARUSIC ◽  
GARY J. KUNKEL ◽  
FERNANDO PORTÉ-AGEL
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Large Eddy Simulation ◽  
Boundary Conditions ◽  
Streamwise Velocity ◽  
New Model ◽  
Eddy Simulation ◽  
Large Eddy

An experimental investigation was conducted to study the wall boundary condition for large-eddy simulation (LES) of a turbulent boundary layer at Rθ = 3500. Most boundary condition formulations for LES require the specification of the instantaneous filtered wall shear stress field based upon the filtered velocity field at the closest grid point above the wall. Three conventional boundary conditions are tested using simultaneously obtained filtered wall shear stress and streamwise and wall-normal velocities, at locations nominally within the log region of the flow. This was done using arrays of hot-film sensors and X-wire probes. The results indicate that models based on streamwise velocity perform better than those using the wall-normal velocity, but overall significant discrepancies were found for all three models. A new model is proposed which gives better agreement with the shear stress measured at the wall. The new model is also based on the streamwise velocity but is formulated so as to be consistent with ‘outer-flow’ scaling similarity of the streamwise velocity spectra. It is therefore expected to be more generally applicable over a larger range of Reynolds numbers at any first-grid position within the log region of the boundary layer.

scholarly journals Assessing Bioinspired Topographies for their Antifouling Potential Control Using Computational Fluid Dynamics (CFD)

2018 ◽  
Vol 152 ◽  
pp. 02004 ◽  
Author(s):  
Jacky Ling ◽  
Felicia Wong Yen Myan
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Extended Period ◽  
Slip Boundary Condition ◽  
Shear Stresses ◽  
Cfd Simulations ◽  
Potential Control ◽  
Slip Boundary ◽  
Computational Fluid Dynamics Cfd ◽  
Wall Shear

Biofouling is the accumulation of unwanted material on surfaces submerged or semi submerged over an extended period. This study investigates the antifouling performance of a new bioinspired topography design. A shark riblets inspired topography was designed with Solidworks and CFD simulations were antifouling performance. The study focuses on the fluid flow velocity, the wall shear stress and the appearance of vortices are to be noted to determine the possible locations biofouling would most probably occur. The inlet mass flow rate is 0.01 kgs-1 and a no-slip boundary condition was applied to the walls of the fluid domain. Simulations indicate that Velocity around the topography averaged at 7.213 x 10-3 ms-1. However, vortices were observed between the gaps. High wall shear stress is observed at the peak of each topography. In contrast, wall shear stress is significantly low at the bed of the topography. This suggests the potential location for the accumulation of biofouling. Results show that bioinspired antifouling topography can be improved by reducing the frequency of gaps between features. Linear surfaces on the topography should also be minimized. This increases the avenues of flow for the fluid, thus potentially increasing shear stresses with surrounding fluid leading to better antifouling performance.

Numerical Investigation of Slip Flow and Heat Transfer in Rotating Rectangular Microchannels

2012 ◽  
Author(s):  
Pratanu Roy ◽  
N. K. Anand ◽  
Debjyoti Banerjee
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Convective Heat Transfer ◽  
Secondary Flow ◽  
Convective Heat ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
Fluid Temperature ◽  
Slip Boundary ◽  
Flow And Heat Transfer

Investigation of fluid flow and heat transfer in rotating microchannels is important for centrifugal microfluidics, which has emerged as an advanced technique in biomedical applications and chemical separations. The pseudo forces namely the centrifugal force and the Coriolis force arising as a consequence of the rotating reference frame change the flow pattern significantly from the parabolic profile in a non-rotating channel. The convective heat transfer process is also influenced by the secondary flow introduced by the rotational effect. Moreover, if the microchannel wall is hydrophobic, slip flow can occur inside the channel when the conventional no slip boundary condition is no longer valid. In this work, we have numerically investigated the flow and heat transfer inside a straight rotating rectangular microchannel in the slip flow regime. A pressure based finite volume technique in a staggered grid was applied to solve the steady incompressible Navier-Stokes and energy equations. It has been observed that, depending on the rotational velocity, different slip velocities are induced at the channel walls. The average fluid temperature increases with the increase of rotation as convective heat transfer mechanism is increased due to the secondary flow. However, the slip boundary condition has a negligible effect on the temperature profiles.

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.

Slip-Flow Pressure Drop in Microchannels of General Cross Section

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
M. Bahrami ◽  
A. Tamayol ◽  
P. Taheri
Keyword(s):  
Boundary Condition ◽  
Pressure Drop ◽  
Cross Section ◽  
Slip Flow ◽  
Homogeneous Boundary Condition ◽  
Slip Boundary Condition ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Cross Sectional ◽  
Slip Boundary

In the present study, a compact analytical model is developed to determine the pressure drop of fully-developed, incompressible, and constant properties slip-flow through arbitrary cross section microchannels. An averaged first-order Maxwell slip boundary condition is considered. Introducing a relative velocity, the difference between the bulk flow and the boundary velocities, the axial momentum reduces to Poisson’s equation with homogeneous boundary condition. Square root of area is selected as the characteristic length scale. The model of Bahrami et al. (2006, “Pressure Drop of Laminar, Fully Developed Flow in Microchannels of Arbitrary Cross Section,” ASME J. Fluids Eng., 128, pp. 1036–1044), which was developed for no-slip boundary condition, is extended to cover the slip-flow regime in this study. The proposed model for pressure drop is a function of geometrical parameters of the channel: cross sectional area, perimeter, polar moment of inertia, and the Knudsen number. The model is successfully validated against existing numerical and experimental data collected from different sources in literature for several shapes, including circular, rectangular, trapezoidal, and double-trapezoidal cross sections and a variety of gases such as nitrogen, argon, and helium.

ELECTROKINETIC SLIP FLOW OF MICROFLUIDICS IN TERMS OF STREAMING POTENTIAL BY A LATTICE BOLTZMANN METHOD: A BOTTOM-UP APPROACH

2007 ◽  
Vol 18 (04) ◽  
pp. 693-700 ◽  
Author(s):  
XIN FU ◽  
BAOMING LI ◽  
JUNFENG ZHANG ◽  
FUZHI TIAN ◽  
DANIEL Y. KWOK
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Slip Boundary ◽  
Surface Energetics ◽  
Boltzmann Method

In traditional computational fluid dynamics, the effect of surface energetics on fluid flow is often ignored or translated into an arbitrary selected slip boundary condition in solving the Navier-Stokes equation. Using a bottom-up approach, we show in this paper that variation of surface energetics through intermolecular theory can be employed in a lattice Boltzmann method to investigate both slip and non-slip phenomena in microfluidics in conjunction with the description of electrokinetic phenomena for electrokinetic slip flow. Rather than using the conventional Navier-Stokes equation with a slip boundary condition, the description of electrokinetic slip flow in microfluidics is manifested by the more physical solid-liquid energy parameters, electrical double layer and contact angle in the mean-field description of the lattice Boltzmann method.

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