Wen-Jei Yang
R. Reznicek S.Mochizuki

Journal of Flow Visualization & Image Processing, vol. 6, pp. 89-94, 1999 Copyright О 1999 by Bcgell House. Inc.


N. Ph Bondarenko, M. Z. Gak, E. Z. Gak,* and M. P. Shapkin
The Agrophysical Research Institute, 14, Grazhdansky Prospect, 195220, Saint-Petersburg, Russia

This work regards a technique of generation and visualization of vortex structures in a thin electrolyte layer. The technique is based on a method of generation of a volumetric magnetohydrodynamic (MHD) force in a fluid affected by constant electric currents and constant magnetic field supplied by the open external magnetic systems of various geometries. Examples of the generation of two- and three-vortex structures are used for consideration of their interaction peculiarities in conditions of variable MHD forces excited in rectangular and triangular flat containers. Discussion is provided to verify that the technique simulating the hydrodynamic phenomena can be broadly encountered in nature and in various applications.
KEY WORDS: visualization, vortex structures, magnetohydrodynamics, modeling.

The studies of nonlinear hydrodynamical processes taking place in the shear flows generated in thin fluid layers are of particular interest for various fields of exploration. To a considerable degree, it is stipulated by sophisticated mathematical procedures that describe a variety of hydrodynamic problems, thus determining the necessity of development of visual methods of study of the phenomena observed. In the first place, it is related to the visualization of the flow structures vs. time for the natural phenomena as well as for their studies in technological equipment and laboratory setups. The laboratory models of vortex structures seem rather attractive because they are suitable not only for visual examination, but also for photography and filming [1-3].

Development of vortex structures of various geometrical parameters in thin fluid layers as well as investigation of their forming and interaction in a laboratory i§ of particular interest for those who are engaged in studies of heat and mass exchange. The laboratory simulation allows repeated reproduction of certain natural phenomena in a controlled environment and reveals some of their aspects that could be missed in field conditions.

Among laboratory methods of vortex generation, such as the sources/sinks method or rotation of the bottom [2,4], major interest is related to the magnetohydrodynamical method of generation of the flows in thin flat electrolyte layers [5-7]. According to this approach, a vortex flow is excited under the influence of intersected electric and magnetic
♦Corresponding author.

90 N. Ph. Bondarenko et al.
fields, whose interaction yields to a field of ponderomotive forces of MHD-nature FMHD = цЦ x BJ where j is a current density vector, Вг is a vertical component of magnetic flux density. Thus, in particular, this method has been implemented in geophysical hydrodynamics for verification of the numerical models that had simulated processes of hydrody-namic instability in atmospheric and oceanic circulation [3], for instance, for examination of interaction between two neighboring cyclones or synoptic vortices. Although the atmosphere has neither lateral walls nor rigid limiting surfaces or multifold differences between the air and water densities, their role could be played by the boundaries that surround more intensive stream flows or vortices of a larger scale.

Two examples of generation of the vortex structures are considered in this work. These are two and three vortices generated in a thin electrolyte layer put in closed vessels of rectangular and triangular forms. Monotonous flow instability as well as the role that the latter could play in natural phenomena are also considered.

Water electrolyte (1.5N CuSO4) has been poured in flat reservoirs. Open magnetic systems have been mounted directly beneath the fluid layer (container bottom). This technique allows attainment of the necessary distribution for a vertical component of a constant magnetic flux Вг in an unlimited horizontal fluid layer. Homogenous distribution for constant current density vector j is formed in the same layer. Variation of FMHD density has been provided by means of/ The electrochemical regimes have been used where current densities were beyond the gas emission zone, i.e.,; < 0.5 A/cm2. Thin fluid layers of a thickness of 3 to 15 mm have been selected; thus, the MHD forces could be developed with spatial-temporary quasi-two-dimensional structure characterized by inflection point on the fluid velocity profile. While using rather thin fluid layers, the bottom and 4aminar boundary layer impacts are reduced to an effective deceleration of the horizontal flows due to friction on an underlaying surface. It results in extension of their stability threshold as shown in [6]. This effect is essential while simulating and studying hydrodynamic instability of the flows. Because the flow species move with velocities 0 to 100 cm/s, visualization with respect to species tracks was ensured by means of small particles (seeds) of lycopodium or by aluminum powder. The powder was piled on the motionless free fluid surface before the experiment. Exposures of 1 to 10 s were used during camera shooting.

Let us begin from the scheme of generation of two vortices in a thin electrolyte layer poured in a rectangular container (Fig. 1).

Container (1) with dimensions 90 x 160 mm was filled with electrolyte (2) to the depth 5 mm and placed on a set of four magnets (3). Each pair of magnets consisted of the square ferrite plates charged axially. Figure  shows the behavior of a vertical component Bv Figure a shows the corresponding behavior of MHD forces as well as the direction of the motion of the vortices.

A similar principle has been applied to the setup designed for generation of three vortices in a container having the form of an equiangular triangle with sides of 160 mm. The magnetic system consisted of two pairs of magnets placed in the triangle corners so that the neutral line of magnetic system was directed along the bisectrix 5 cm from the corner. Electrodes have been mounted to container lateral walls 3 cm from the corner.

Vortex Structures in Electrolytes and Modeling of Natural Phenomena

Fig. 1 Layout of generation of two-vortex structures of equal intensity, (a) Setup: 1—rectangular container, 2—electrolyte; 3—magnetic system composed of two rectangular magnets; 4—electrodes, (b) Вг distribution along y-axis in the center of the magnetic systems.

Depicted in Fig. la, experimental setup allows the creation of two pairs of forces in the flat layer, thus exciting two vortices, whose strength, size, and direction of rotation with

N. Ph Bondarenko et al.

angular velocity со are defined by j and Br As follows from the experiment, when the vortices rotate in opposite directions, vorticity structure preserves its stability, although in natural conditions the vortices diverge. In our experiment it does not occur because the container width restricts vortex dimensions.
Figure 2 demonstrates a different picture. Vortices are rotating in the same direction. At first, the third vortex appears, which is analogous to the vortex layer (Fig. 2a). With increasing current density, the loss of stability can be observed (Fig. 2b), then vortices merge, resulting in the united vortex with dimensions corresponding to the container size. Meanwhile, stagnation zones, which in a form of small vortices occupy container corners,

Fig. 2 Photograph of two-vortex flows of the same strength and direction. Camera Zenit. Film Micrat-300. Exposure 2 s. (a)j < 10 mA/cm1. (b) 10 mA/cm2
Vortex Structures in Electrolytes and Modeling of Natural Phenomena

can be clearly observed. It may be supposed that the presence of the third vortex among primary ones determines stability of the flow behavior.
A similar picture takes place in case of generation of three vortices in a triangular container (Fig. 3). Three vortices can be seen in the container corners (Fig. 3a); they

Fig. 3 Photograph of three-vortex flows of the same strength and direction. Camera Zcnit. Film Micrat-300. Exposure 2 s. (a)j < 15 mA/cm:. (6) 15 mA/cm:
N. Ph Bondarenko et al.
increase with current (Fig. 3b) and further merge with the united effective vortex structure with dimensions corresponding to the container size (Fig. 3c). It should also be noted that the vortices of smaller size originate in the container corners.

It may be expected that this effect can obviously simulate the phenomena of evolution of the vortex flows during three neighboring cyclones, which is rather difficult to examine in natural conditions. Comparison with this picture and other similar ones made earlier may Be provided also using aerospace shooting of dust storms, interaction of synoptic vortices, cyclone generation, and typhoon origination [8]. Thus, in particular, the structures of triangular form are often met on the maps of oceanic and atmospheric circulations. By the way, these results may be applied to the studies of generation of turbulence in the flows in rectangular tubes, which has not been investigated completely up to now.

These experiments are helpful for modeling and study of complicated processes of energy transfer in quasi-two-dimensional vortex flows having both small and large scales, which is illustrated by the flows characterized by «negative viscosity» that may be observed in nature and in laboratory experiments [9,10].

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