Momentum transfer within a porous medium. II. Stress boundary condition

2014 ◽  
Vol 26 (12) ◽  
pp. 123102 ◽  
Author(s):  
Mario Minale
Keyword(s):  
Boundary Condition ◽  
Porous Medium ◽  
Momentum Transfer ◽  
Stress Boundary Condition ◽  
Stress Boundary

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 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.

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.

An equatorial boundary layer

1972 ◽  
Vol 56 (2) ◽  
pp. 193-200 ◽  
Author(s):  
J. M. Dowden
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Velocity Field ◽  
Linear Equation ◽  
Closed Form ◽  
Equations Of Motion ◽  
Ekman Layer ◽  
Parameter Range ◽  
Stress Boundary Condition ◽  
Stress Boundary

The singularity of the Ekman layer at the equator of a rotating gravitating sphere makes it difficult to satisfy a prescribed stress boundary condition at the surface of a layer of liquid on the sphere. The equations of motion are investigated for a homogeneous ocean with vertical and lateral eddy viscosities. The horizontal Coriolis terms are not neglected. A linear equation for the boundary layer is obtained and a solution of the equation for the boundary-layer part of the velocity field is found in closed form. This is valid in a parameter range which includes the previous solutions of Stewartson and Gill as limiting cases.

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