scholarly journals Fluid Driven by Tangential Velocity and Shear Stress: Mathematical Analysis, Numerical Experiment, and Implication to Surface Flow

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
H. S. Tang ◽  
L. Z. Zhang ◽  
J. P.-Y. Maa ◽  
H. Li ◽  
C. B. Jiang ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Shear Stress ◽  
Boundary Conditions ◽  
Steady Flow ◽  
Tangential Velocity ◽  
Surface Flow ◽  
Parallel Plates ◽  
Moving Plate ◽  
Stress Boundary Condition ◽  
Stress Boundary

This paper investigates behaviors of flows driven by tangential velocity and shear stress on their boundaries such as solid walls and water surfaces. In a steady flow between two parallel plates with one of them in motion, analytic solutions are the same when a velocity and a shear stress boundary condition are applied on the moving plate. For an unsteady, impulsively started flow, however, analysis shows that solutions for velocity profiles as well as energy transferring and dissipation are different under the two boundary conditions. In an air-water flow, if either a velocity or a stress condition is imposed at the air-water interface, the problem becomes ill-posed because it has multiple solutions. Only when both of the conditions are specified, it will have a unique solution. Numerical simulations for cavity flows are made to confirm the theoretical results; a tangential velocity and a shear stress boundary condition introduce distinct flows if one considers an unsteady flow, whereas the two conditions lead to a same solution if one simulates a steady flow. The results in this paper imply that discretion is needed on selection of boundary conditions to approximate forcing on fluid boundaries such as wind effects on surfaces of coastal ocean waters.

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.

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.

Analytic stress solution for a circular tunnel in half plane with a concentrated force

2019 ◽  
Vol 24 (12) ◽  
pp. 3862-3879
Author(s):  
Hui Cai ◽  
Ai-zhong Lu ◽  
Yao-cai Ma
Keyword(s):  
Boundary Condition ◽  
Stress Distribution ◽  
Half Plane ◽  
Analytic Functions ◽  
Surrounding Rock ◽  
Circular Tunnel ◽  
Concentrated Force ◽  
Stress Solution ◽  
Stress Boundary Condition ◽  
Stress Boundary

An analytic stress solution is presented for a circular tunnel problem in a half plane with a concentrated force acting on any position in the field under gravity. The solution uses the complex variable method and the power series method. The influence of the unbalanced force system on the tunnel boundary is considered. The relationship between two analytic functions is established by using surface stress boundary condition. The analytic functions can be determined from the tunnel stress boundary condition. Based on the principle of superposition, the stresses of the surrounding rock can be calculated by superimposing three partial solutions which are obtained separately. The examples give contour plots of the principal stresses in the surrounding rock, focus on the stress distribution on the ground surface and the tunnel boundary and analyze the effect on the stress distribution of some main parameters.

Screw Dislocations in a Three-Phase Composite Cylinder Model With Interface Stress

2008 ◽  
Vol 75 (4) ◽  
Author(s):  
Q. H. Fang ◽  
Y. W. Liu ◽  
P. H. Wen
Keyword(s):  
Boundary Condition ◽  
Classical Case ◽  
Interface Stress ◽  
Composite Cylinder ◽  
Screw Dislocations ◽  
Three Phase ◽  
Cylinder Model ◽  
The Matrix ◽  
Stress Boundary Condition ◽  
Stress Boundary

A three-phase composite cylinder model is utilized to study the interaction between screw dislocations and nanoscale inclusions. The stress boundary condition at the interface between nanoscale inclusion and the matrix is modified by incorporating surface/interface stress. The explicit solution to this problem is derived by means of the complex variable method. The explicit expressions of image forces exerted on screw dislocations are obtained. The mobility and the equilibrium positions of the dislocation near one of the inclusions are discussed. The results show that, compared to the classical solution (without interface stress), more equilibrium positions of the screw dislocation may be available when the dislocation is close to the nanoscale inclusion due to consider interface stress. Also, the mobility of the dislocation in the matrix will become more complex than the classical case.

scholarly journals The Casimir effect with quantized charged scalar matter in background magnetic field

2014 ◽  
Vol 29 (09) ◽  
pp. 1450052 ◽  
Author(s):  
Yu. A. Sitenko ◽  
S. A. Yushchenko
Keyword(s):  
Magnetic Field ◽  
Boundary Condition ◽  
Boundary Conditions ◽  
Casimir Force ◽  
Matter Field ◽  
Particle Energy ◽  
Parallel Plates ◽  
Charged Scalar ◽  
Scalar Matter ◽  
Background Magnetic Field

We study the influence of a background uniform magnetic field and boundary conditions on the vacuum of a quantized charged massive scalar matter field confined between two parallel plates; the magnetic field is directed orthogonally to the plates. The admissible set of boundary conditions at the plates is determined by the requirement that the operator of one-particle energy squared be self-adjoint and positive-definite. We show that, in the case of a weak magnetic field and a small separation of the plates, the Casimir force is either attractive or repulsive, depending on the choice of a boundary condition. In the case of a strong magnetic field and a large separation of the plates, the Casimir force is repulsive, being independent of the choice of a boundary condition, as well as of the distance between the plates.

Fluid Slip of Flow Past a Hydrophobic Wall Sphere

2004 ◽  
Author(s):  
Takao Fujita ◽  
Keizo Watanabe
Keyword(s):  
Boundary Condition ◽  
Drag Reduction ◽  
Flow Visualization ◽  
Flow Characteristics ◽  
Flow Patterns ◽  
Liquid Interface ◽  
Solid Boundary ◽  
Stress Boundary Condition ◽  
Sphere Drag ◽  
Stress Boundary

The possibility of fluid slip has received considerable attention in recent years. Laminar drag reduction is achieved by using a hydrophobic wall with fluid slip. Fluid slip is closely related to the gas-liquid interface formed at a solid surface with many fine grooves. The friction generated by the solid boundary is modified considerably because the gas-liquid interface provides a zero-shear stress boundary condition. The purpose of this study is to experimentally clarify the flow characteristics and drag reduction of a hydrophobic wall sphere by visualizing flow and by measuring the drag. In addition, the flow patterns were numerically analyzed by applying a wet boundary condition for fluid slip. The flow visualization results showed that the Vortex Loop was not exist at Re < 400 in the hydrophobic wall sphere and the separation point moved downstream compared with that of a conventionally smooth sphere. Drag reduction occurred in the flow and the maximum drag reduction ratio was 14.6% at Re=93.2. In this simulation, the flow patterns for the numerical simulation results agreed with those of the flow visualization results.

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