The nonlinear flow field induced by a point force in the presence of a plane wall

1981 ◽  
Vol 376 (1766) ◽  
pp. 435-450 ◽  
Keyword(s):  
Flow Field ◽  
Stagnation Point ◽  
Plane Wall ◽  
Point Force ◽  
Nonlinear Flow ◽  
Unit Force ◽  
Closed Loops ◽  
Meridian Section ◽  
Continuous Application ◽  
Section Form

A nonlinear solution is constructed representing the steady flow field generated by the continuous application of a constant point force of magnitude F 0 in an incompressible fluid that is bounded by a fixed plane wall. The force is applied at a fixed distance from the wall, is perpendicular to the wall and directed towards it. The streamlines in a meridian section form closed loops which nest at a stagnation point and it is found that as F 0 increases this stagnation point is displaced towards the wall. It is also found that as F 0 increases the total volume flow per unit force decreases.

The axisymmetric flow field induced by a point force in the presence of a plane wall

1982 ◽  
Vol 380 (1779) ◽  
pp. 349-357 ◽  
Keyword(s):  
Flow Field ◽  
Stagnation Point ◽  
Axisymmetric Flow ◽  
Plane Wall ◽  
Point Force ◽  
Nonlinear Flow ◽  
Volume Flux ◽  
Closed Loops ◽  
Meridian Section ◽  
Section Form

In this paper we consider a numerically constructed solution concerning the steady nonlinear flow field generated by a point force of magnitude F 0 in an incompressible fluid bounded by a plane wall. The force is applied at a fixed distance from the wall and is perpendicular to it. The streamlines in a meridian section form closed loops which nest at a stagnation point and it is found that as F 0 increases this stagnation point is displaced towards or away from the wall depending on whether the force is pointing towards or away from it. It is also found that as F 0 increases the total volume flux per unit force decreases when the force is pointing towards the wall and increases when the force is pointing in the opposite direction. For instance when F 0 is 150 v 2 ρ , where v denotes the coefficient of kinematic viscosity and ρ the fluid density, the total volume flux for the case where the force points away from the wall is several times that for the case where the force points towards the wall.

Magnetohydrodynamic flow due to the discharge of an electric current in a hemispherical container

1976 ◽  
Vol 73 (4) ◽  
pp. 641-650 ◽  
Author(s):  
C. Sozou ◽  
W. M. Pickering
Keyword(s):  
Free Surface ◽  
Velocity Field ◽  
Flow Field ◽  
Electric Current ◽  
Cross Section ◽  
Analytic Solution ◽  
Closed Loops ◽  
Slow Viscous Flow ◽  
Axial Cross Section ◽  
Section Form

In this paper we consider the flow field induced in an incompressible viscous conducting fluid in a hemispherical bowl by a symmetric discharge of electric current from a point source at the centre of the plane end of the hemisphere. This plane end is a free surface. We construct an analytic solution for the slow viscous flow and a numeriacl solution for the nonlinear problem. The streamlines in an axial cross-section form two sets of closed loops, one on either side of the axis. Our computations indicate that, for a given fluid, when the discharged current reaches a certain magnitude the velocity field breaks down. This breakdown probably originates at the vertex of the hemispherical container.

Development of the flow field of a point force in an infinite fluid

1979 ◽  
Vol 91 (3) ◽  
pp. 541-546 ◽  
Author(s):  
C. Sozou
Keyword(s):  
Flow Field ◽  
Cross Section ◽  
Kinematic Viscosity ◽  
Point Force ◽  
Linear Flow ◽  
Closed Loops ◽  
Stagnation Points ◽  
Dipole Structure ◽  
Field Lines ◽  
Set Up

By means of similarity principles an analytical solution is constructed for the development of the linear flow field due to the instantaneous application of a constant point force in an infinite liquid. If the force is applied at the origin O and if ν denotes distance from O, ν denotes the coefficient of kinematic viscosity of the fluid and t the time from the application of the force, the solution constructed exhibits the following features. Initially the flow field set up has a dipole structure with centre at O and axis along the direction of the impressed force. At a station r this dipole structure persists so long as 4νt [Lt ] r2. In an axial cross-section the field lines form two sets of closed loops about two stagnation points in the equatorial plane. The stagnation points occur at r = 1.76(νt)½ and thus propagate to infinity with speed 0.88(ν/t)½. The steady state is reached algebraically.

The development of magnetohydrodynamic flow due to an electric current discharge

1975 ◽  
Vol 70 (3) ◽  
pp. 509-517 ◽  
Author(s):  
C. Sozou ◽  
W. M. Pickering
Keyword(s):  
Flow Field ◽  
Electric Current ◽  
Stagnation Point ◽  
Cross Section ◽  
Kinematic Viscosity ◽  
Magnetohydrodynamic Flow ◽  
Dimensionless Variable ◽  
Closed Loops ◽  
Developing Flow ◽  
Set Up

The development of the magnetohydrodynamic flow field due to the discharge of an electric current J0 from a point on a plate bounding a semi-infinite viscous incompressible conducting fluid is considered. The flow field is the response of the fluid to the Lorentz force set up by the electric current and the associated magnetic field. The problem is formulated in terms of the dimensionless variable (vt)½/r and solved numerically. Here ν is the coefficient of kinematic viscosity, t the time from the application of the electric current and r the distance from the discharge. It is shown that the streamlines of the developing flow field in a cross-section through the axis of the discharge are closed loops about a stagnation point. As the flow field develops, the stagnation point moves to infinity along a ray emanating from the discharge with a speed proportional to t−½. The steady state, within a distance r from the discharge, is practically established when t = r2/ν.

The round laminar jet: the development of the flow field

1977 ◽  
Vol 80 (4) ◽  
pp. 673-683 ◽  
Author(s):  
C. Sozou ◽  
W. M. Pickering
Keyword(s):  
Flow Field ◽  
Stagnation Point ◽  
Dipole Axis ◽  
Dimensionless Variable ◽  
Closed Loops ◽  
Laminar Jet ◽  
Variable Λ ◽  
Developing Flow ◽  
Straight Line ◽  
Axis Of Symmetry

The development of the flow field of a jet emanating from a point source of momentum in an infinite incompressible fluid of density σ is considered. The flow field is assumed to be due to the application of a constant force F0 at the origin. The problem is formulated in terms of the dimensionless variable λ = (vt)½/r, where v is the kinematic viscosity of the fluid, t the time from the application of the force and r the distance from the origin. At a station r the flow field is dipolar, with the dipole axis in the direction of F0, for all t satisfying the inequalities vt Lt; r2 and F0t2 [Lt ] 4πρr4. Also, at a given time t the streamlines of the developing flow field in a section through the axis of symmetry of the problem form closed loops about a stagnation point. If this occurs at λ = λm, the stagnation point propagates to infinity, along a straight line emanating from the origin, with speed v½/2λmt½, where λm = λm(F0) decreases as F0 increases. The larger F0 is the faster the steady state is established.

The motion of a droplet subjected to linear shear flow including the presence of a plane wall

1995 ◽  
Vol 302 ◽  
pp. 45-63 ◽  
Author(s):  
W. S. J. Uijttewaal ◽  
E. J. Nijhof
Keyword(s):  
Shear Flow ◽  
Flow Field ◽  
Theoretical Models ◽  
Boundary Integral ◽  
Plane Wall ◽  
Time Dependent ◽  
Fluid Inertia ◽  
Linear Shear ◽  
Material Element ◽  
Migration Velocities

A fluid droplet subjected to shear flow deforms and rotates in the flow. In the presence of a wall the droplet migrates with respect to a material element in the undisturbed flow field. Neglecting fluid inertia, the Stakes problem for the droplet is solved using a boundary integral technique. It is shown how the time-dependent deformation, orientation, circulation and droplet viscosity. The migration velocities are calculated in the directions parallel and perpendicular to the wall, and compared with theoretical models and expeeriments. The results reveal some of the shortcomings of existiong models although not all diserepancies between our calculations and known experiments could be clarified.

Force on a Small Particle Attached to a Plane Wall in a Hiemenz Straining Flow

2012 ◽  
Vol 134 (11) ◽  
Author(s):  
A. B. Maynard ◽  
J. S. Marshall
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Reynolds Numbers ◽  
Lower Surface ◽  
Ring Structure ◽  
Plane Wall ◽  
Small Reynolds Numbers ◽  
Particle Force ◽  
Volume Method ◽  
Excellent Accuracy

The force acting on a spherical particle fixed to a wall and immersed in an axisymmetric straining flow is examined for small Reynolds numbers. The steady, incompressible flow field is computed using an axisymmetric finite-volume method over conditions spanning five decades in the Reynolds number. The flow is characterized by the formation of a vortex ring structure in the wedge region formed between the particle lower surface and the plane wall. A power law expression for the dimensionless particle force is obtained as a function of the Reynolds number, which is found to hold with excellent accuracy for Reynolds numbers below about 0.1.

Crossflow Over a Porous Circular Cylinder With Surface Blowing: CFD Analysis With Experimental Validation

2012 ◽  
Author(s):  
T. H. Reif ◽  
F. A. Kulacki
Keyword(s):  
Circular Cylinder ◽  
Flow Field ◽  
Stagnation Point ◽  
Test Section ◽  
Free Stream ◽  
Absolute Error ◽  
Secondary Flows ◽  
Test Case ◽  
Positional Error ◽  
Rear Stagnation Point

Crossflow over a porous circular cylinder, with uniform blowing at the surface, was investigated experimentally and numerically. Two free stream conditions, Reynolds numbers 4,100 and 6,200, and five dimensionless blowing rate parameters (ratio of surface blowing to free stream velocity), 0.000 to 0.190, were studied experimentally. For simplicity, results for only one Reynolds number and three blowing cases are presented. A low speed wind tunnel was designed and constructed to give time-smoothed average velocities in the range of 61–122 cm/s. The tunnel was calibrated prior to the study. Velocity and pressure profiles were uniform up to 3.81 cm from the walls of the test section. Turbulence intensity, measured at the center of the test section, was 3.0% with an absolute error of 0.5%. Using hot wire anemometry, time-smoothed velocity profiles were measured at several radial and angular positions from the front to the rear stagnation point. The maximum absolute error in the velocity measurements was 12 cm/s and the positional error of the probe was 0.00254 cm. The numerical study employed the finite element method. The flow field was modeled as two-dimensional with half-symmetry. The unsteady, turbulent (k/ε) model had 2,160 elements and 2,287 nodes. Convergence and laminar flow was verified. When blowing was present, the numerical solution was found to give excellent agreement with the experiments in the entire flow field. For the no blowing test case, the agreement with the experiments was also excellent up to 20 deg from the rear stagnation point. Flow visualization, using smoke, was used to qualitatively study the large scale secondary flows in the wake region. These results helped explain the poorer agreement for the no blowing test case.

scholarly journals Assessment of the Nonlinear Flow Characteristic of Water Inrush Based on the Brinkman and Forchheimer Seepage Model

Water ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 855 ◽  
Author(s):  
Yi Xue ◽  
Yang Liu ◽  
Faning Dang ◽  
Jia Liu ◽  
Zongyuan Ma ◽  
...  
Keyword(s):  
Flow Field ◽  
Water Flow ◽  
Construction Projects ◽  
Underground Mining ◽  
Fractured Rock ◽  
Flow Behavior ◽  
Water Inrush ◽  
Nonlinear Flow ◽  
Fault Permeability ◽  
Forchheimer Flow

Underground fault water inrush is a hydrogeological disaster that frequently occurs in underground mining and tunnel construction projects. Groundwater may pour from an aquifer when disasters occur, and aquifers are typically associated with fractured rock formations. Water inrush accidents are likely to occur when fractured rock masses are encountered during excavation. In this study, Comsol Multiphysics, cross-platform multiphysics field coupling software, was used to simulate the evolution characteristics of water flow in different flow fields of faults and aquifers when water inrush from underground faults occurs. First, the Darcy and Brinkman flow field nonlinear seepage models were used to model the seepage law of water flow in aquifers and faults. Second, the Forchheimer flow field was used to modify the seepage of fluid in fault-broken rocks in the Brinkman flow field. In general, this phenomenon does not meet the applicable conditions of Darcy’s formula. Therefore, the Darcy and Forchheimer flow models were coupled in this study. Simulation results show that flow behavior in an aquifer varies depending on fault permeability. An aquifer near a fault is likely to be affected by non-Darcy flow. That is, the non-Darcy effect zone will either increase or decrease as fault permeability increases or decreases. The fault rupture zone that connects the aquifer and upper roadway of the fault leads to fault water inrush due to the considerably improved permeability of the fractured rock mass.

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