Sound transmission and generation in ducts with flow

Weld pool fluid flow can affect the penetration of the resultant weld significantly. In this work, the computer simulation of weld pool fluid flow and its effect on weld penetration was carried out. Steady-state, 2-dimensional heat and fluid flow in stationary arc welds were computed, with three driving forces for fluid flow being considered: the buoyancy force, the electromagnetic force, and the surface tension gradient at the weld pool surface. The computer model developed agreed well with available analytical solutions and was consistent with weld convection phenomena experimentally observed by previous investigators and the authors. The relative importance of the influence of the three driving forces on fluid flow and weld penetration was evaluated, and the role of surface active agents was discussed. The effects of the thermal expansion coefficient of the liquid metal, the current density distribution in the workpiece, and the surface tension temperature coefficient of the liquid metal on weld pool fluid flow were demonstrated. Meanwhile, a new approach to free boundary problems involving simultaneous heat and fluid flow was developed, and the effort of computation was reduced significantly.

Fluid flow and weld penetration in stationary arc welds

The motion of two drops in a uniform electric field is considered using the leaky dielectric model. The drops are assumed to have no native charge and a dielectrophoretic effect favours translation of the drops toward one another. However, circulatory flows that stem from electrohydrodynamic stresses may either act with or against this dielectrophoretic effect. Consequently, both prolate and oblate drop deformations may be generated and significant deformation occurs near drop contact owing to enhancement of the local electric field. For sufficiently widely spaced drops, electrohydrodynamic flows dominate direct electrical interactions so drops may be pushed apart, though closely spaced drops almost always move together as a result of the electrical interaction or deformation.

Electrohydrodynamic deformation and interaction of drop pairs

The paper reviews striking features of swirling flows—collapse, swirl generation, vortex breakdown, hysteresis, and axisymmetry breaking—and the mechanisms involved with the help of conical similarity solutions of the Navier-Stokes equations. The strong accumulation of axial and angular momenta, observed in tornadoes and flows over delta wings, corresponds to collapse, i.e. the singularity development in these solutions. Bifurcation of swirl explains the threshold character of swirl development in capillary and electrovortex flows. Analytical solutions for fold catastrophes and hysteresis reveal why there are so few stable states and why the jump transitions between the states occur—features typical of tornadoes, of flows over delta wings, and in vortex devices. Finally, the divergent instability explains such effects as the splitting of a tornado and the development of spiral branches in tree and near-wall swirling flows.

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Collapse, symmetry breaking, and hysteresis in swirling flows

A dynamic model of drop detachment in gas metal arc welding is presented for low and moderate welding currents in an argon-rich plasma. Simulations performed with this model are compared with extensive experimental measurements of constant-current welding images and with limited experimental measurements of pulsed-current welding images. The comparisons indicate that the experimental axial magnetic forces are much less potent than the calculated axial magnetic forces when welding-current transients are not present. To explain this finding the hypothesis that internal flows are able to develop under the relatively quiescent conditions that exist during drop development in constant-current welding is advanced.

https://iopscience.iop.org/article/10.1088/0022-3727/31/1/014/pdf

A dynamic model of drops detaching from a gas metal arc welding electrode

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.

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

In this paper we consider the flow field induced in an incompressible viscous conducting fluid, occupying the interior of a right circular cone, by an electriccurrent source situated at the vertex of the cone. We assume that the velocity field is small and its effect on the electromagnetic field is negligible. A similarity solution is obtained for the non-linear problem. This solution is an adaptation of Slezkin's solution for the momentum transfer through a viscous jet and, apart from the numerical solution of a Riccati type of equation, is exact. In particular, we investigate the case when the half angle of the cone is ½π and the fluid occupies the whole space on one side of an infinite plane. We also consider the corresponding inviscid flow problem that was recently investigated by another author and suggest that the solution obtained is not physically realistic.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112071000375

On fluid motions induced by an electric current source

In this paper we consider the flow field generated by a uniform electrostatic field in and about a pair of identical liquid drops immersed in a conducting fluid. It is assumed that the undisturbed electric field is parallel to the line joining the centres of the two drops. The flow field is due to the tangential electric stress over the surfaces of the drops and here this stress and the flow field are expressed in terms of bispherical harmonics. When the distance between the centres of the drops is many drop diameters the tangential electric stress and the flow field in and about one drop are unaffected by the presence of the other drop, as expected. When the distance between the centres of the drops is of the order of two drop diameters there is a substantial modification in the tangential electric stress at the surfaces of the drops and in the induced flow field, especially in the region between the planes through the drop centres perpendicular to the undisturbed electric field.

Electrohydrodynamics of a pair of liquid drops

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.

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

In this paper we consider the Stokes flow field generated in a hemispheroidal container by the axisymmetric discharge of an electric current. The current is discharged from a circular electrode which is at the centre of the equatorial plane of the spheroid. The electrode is assumed to be at a constant potential. The equatorial radius of the spheroid is a and that of the electrode is k, the annulus $k$ $\leq $ $r$ $\leq $ $a$ being a free surface. For a given container depth it is shown that as k increases the intensity of the flow field decreases and when the depth of the container is comparable to k the intensity of the flow field is only a small fraction of that associated with the point electrode case. As one might expect, the vorticity has a singularity at the rim of the electrode. When the width of the annulus forming the free surface is small, relative to the radius of the electrode, an eddy is formed about the rim of the electrode. As the annulus increases the eddy decreases in size until it eventually disappears.

C. Sozou

Papers

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

On fluid motions induced by an electric current source

Electrohydrodynamics of a pair of liquid drops

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

Magnetohydrodynamic flow in a container due to the discharge of an electric current from a finite size electrode