RU2305869C2 - Method of demonstration of vortex resonance at spin-up and registering electrode - Google Patents

Abstract

FIELD: hydrodynamics.

SUBSTANCE: method can be used as educational aid when studying transient processes in rotating fluid. Redox system is solved in fluid; fluid is poured into reservoir made in form of body of rotation with vertical axis of symmetry; registering electrode and ancillary electrode, which area exceeds the registering electrode's active area, are submerged into fluid. Both electrodes are connected to opposite poles of dc voltage supply; registering electrode is fixed independently on reservoir; reservoir is driven into rotation to work with permanent angular speed. Electric current flowing through registering electrode is measured as function of time. Beginning of increment in current is used as sign of coming of front of rotation of fluid from reservoir's wall to place of disposition of active part of registering electrode. Time delay in current rise is measured after reservoir begins to rotate. Measured delay time is used to judge on radial speed of front of rotation of fluid. Disturbance in monotonous rise of current in time, which rise has shape of current oscillations, is presented as sign axial symmetry of flow due to formation of axes oriented in opposition. Period of oscillation of current is compared with period of rotation of reservoir. Coincidence of both periods is interpreted as resonance with vortex localization in coordinate system, which coordinate system rotates together with reservoir. Registering electrode is made in form of electro-conducting band. Band has active and console parts along its length; both parts are submerged into fluid. Console part is covered with isolating film. One end of console part is fastened to vertical rod for putting rod in coincidence with axis of rotation of reservoir. End of console part, remote from rod, has longitudinal curve and it adjoins active part in form of plate oriented along axis of rotation of reservoir.

EFFECT: demonstration of vortex resonance phenomenon.

23 cl, 55 dwg

Description

The invention relates to the field of hydrodynamics and can be used as a visual aid in the study of transients in a rotating fluid.

Spin-up is defined as the process of establishing stationary rotation of a fluid (Greenspan X. Theory of rotating fluids, Moscow, Gidrometeoizdat, 1975, p. 36).

There is a method of demonstrating spinap, including the suspension of aluminum powder in a liquid, pulsating a transparent cylindrical tank with this liquid into rotation with a constant angular velocity around the axis of symmetry of the tank, illuminating the tank with a slit light source, and photographing the front of rotation of the liquid in transmitted light (ibid., p.10).

The study of spinap is also described by visual observation of particles suspended in a liquid (E.H. Wedemeyer, J. of Fluid Mechanics, 1964, vol. 20, p. 383-399).

In an embodiment of the known method, the front of rotation of a liquid is recorded by laser irradiation of a stratified fluid in the form of a concentrated salt solution, the density of which varies along the height of a cylindrical tank (JBFlor, M.Ungarish, JWMBush, J. of Fluid Mechanics, 2002, vol. 472, p. 51-82).

Resonance phenomena during spinup are still not described in the literature, since they are not accessible to observation by known methods.

The external influence during spin is a stepwise pulse of rotation of the tank, and the reaction of the observed system is the gradual unwinding of the liquid to the state of solid state rotation, in which all parts of the liquid acquire the angular velocity of the tank. During this time, the tank makes dozens of revolutions.

In contrast to the known methods, the proposed method allows to detect a vortex, the axis of which is ahead of the liquid and in angular velocity is close to the reservoir until synchronous rotation with it. The proximity of the angular velocities of the axis of the vortex and the reservoir with the possibility of an exact equality of these velocities allows us to define the detected phenomenon as vortex resonance. The vortex violates the axial symmetry of the fluid rotation.

The paradox of the discovered phenomenon is that the vortex as a whole moves synchronously with a round tank that does not have significant defects. The experimental conditions exclude the trivial mechanical engagement of the vortex.

Along with the exact resonance, relatively small deviations from it are also observed, in which the vortex slowly slides along the tank wall, which additionally indicates the absence of adhesion to the wall. From experiments it follows that vortex resonance is a property of fluid flow in a reservoir with an ideal shape of a body of revolution. It occurs in a certain range of conditions, characteristic, in particular, for planets with solid nuclei in a liquid medium.

The unusual and practical significance of the vortex resonance makes it expedient to create favorable conditions for it and to carry out its visual demonstration as a separate phenomenon. The technical result of this invention is a joint solution to these two problems.

The specified technical result is achieved by dissolving the redox system in the liquid, pouring the liquid into the tank, which has the form of a body of revolution with a vertical axis of symmetry, immersing the recording electrode and an auxiliary electrode that exceeds its active area, and connecting these electrodes to the opposite poles of the source DC voltage, fix the recording electrode independently of the tank, pulse start the tank in rotation with a constant angular velocity By measuring the electric current through the recording electrode as a function of time, the beginning of the current rise is used as a sign of the arrival of the front of rotation of the liquid from the tank wall to the location of the recording electrode, the delay time of the current rise from the beginning of the rotation of the tank is measured, the radial velocity of the front is measured by the measured delay time fluid rotation, a periodic violation of the monotonicity of current growth over time, having the form of current oscillations, is presented as a sign of axial asymmetry of the flow due to the formation of oppositely directed vortices, ahead of the rotation of the liquid, compare the period of current oscillations with the period of rotation of the tank, and the coincidence of these periods is interpreted as resonance with the localization of the vortices in the coordinate system rotating with the tank,

The period of current fluctuations is measured as the minimum time interval between similar current extremes in form, and the sign of the coincidence of the period of current fluctuations with the period of rotation of the tank is considered to be the limitation of their difference from above by a value of 20% of the period of rotation of the tank.

The number of vortices in the horizontal plane passing through the active part of the recording electrode is determined by the number of current extremes for one period of current oscillations. The direction of fluid circulation in the vortex relative to the direction of rotation of the reservoir is determined by the form of the extremum, and the maximum and minimum currents correspond to the associated (with the coincidence of the indicated directions) and counter (with the opposite directions) vortices.

The circulation of a fluid in a vortex means its own rotation of the vortex - its contribution to the total movement of the fluid in the reservoir. Vortices form an asymmetric component of fluid motion, which is superimposed on symmetric rotation.

The mutual position of the axis of the vortices in the horizontal plane passing through the active part of the recording electrode is determined by the ratio of the duration of the rise and fall of the current between the extrema.

A tank with a spherical wall is used, while the active part of the recording electrode is placed at the level of the largest diameter section of the tank, which coincides with the equatorial plane.

The active part of the recording electrode is made in the form of a plate with a flat or cylindrical surface and this plate is oriented parallel to the axis of symmetry of the tank. The rotation of the tank is carried out sequentially in two opposite directions.

A cylindrical tank with height-adjustable internal partitions is also used, and a recording electrode is placed between the partitions.

The rotation of the tank is stopped before the start of the current rise, the measured time of the delay of the current rise is compared with the delay time measured during the rotation of the tank, and based on the coincidence of the measured times, it is concluded that the radial velocity of the front of rotation of the liquid is independent of the azimuthal speed of the liquid after stopping the tank.

Before the pulse start of the fluid reservoir, an initial rotation is reported. The recording electrode circuit is opened and closed during the rotation of the tank.

Use plates of different lengths, orient them along the flow, measure the steady-state values of the limiting currents during rotation of the tank with two periods that ensure laminar flow around the plates, and calculate the exponent in the equality

where T _r1 , T _r2 - periods of rotation of the tank,

,

- соответствующие предельные токи,

,

- corresponding limiting currents,

n is an exponent

Based on the calculation, they show that the exponent exceeds 2 and increases with decreasing plate length along the flow, which is associated with a thickening of the boundary layer on the plate due to the formation of a region of separation of the liquid flow.

In the case of a monotonous decrease in the average current limit per revolution of the reservoir, the recording electrode is shifted by a pulse with a return to its original position and the degree of increase in the limit current is observed, which is associated with a pulsed reduction in the volume of the flow separation region on the plate.

The intervals of rotation of the tank with a constant angular velocity periodically alternate with equal to them in time intervals of the immobility of the tank. At the same time, the duration of the rise and fall of the current between steady-state extreme values is compared on the dependence of current on time. It is shown in such a way that under the conditions of the indicated intermittent rotation of the tank, a rise in current and, accordingly, an increase in the fluid velocity occur faster than the decline of these values. The recording electrode is fixed with the possibility of rotation relative to the axis of symmetry of the tank. The second recording electrode is immersed in a liquid and currents through both recording electrodes are measured simultaneously.

The recording electrode used to demonstrate spinap is made in the form of an electrically conductive tape placed in a tank with liquid, along the length of the tape there are cantilever and active parts immersed in the liquid, the cantilever part is covered with an insulating film, one of the ends of the cantilever part is fastened with a vertical rod with the possibility of alignment of the rod with the axis of rotation of the tank, the end of the cantilever portion remote from the rod has a longitudinal bend and is adjacent to the active part, which includes a plate oriented along the bp axis scheniya tank.

The tape is symmetrical about a plane passing through the axis of rotation of the tank. In addition, the tape may include elements that are part of the body of rotation. In one embodiment of the recording electrode, the plate is flat with the possibility of applying strips of insulating coating to the plate, as well as with the possibility of completely isolating one of the sides of the plate. In another embodiment, the end of the cantilever portion of the tape remote from the rod is connected to the rod by a fiber loop.

The insulating film covering the cantilever portion of the tape contains chloroprene rubber.

The invention is based on a combination of two functions of a recording electrode: 1) transmission of electric current, 2) selection of the type of symmetry of fluid rotation. The second of these electrode functions is fundamentally new.

The relatively small perturbations introduced into the flow by the electrode are amplified by the flow and transfer the liquid to a stable state of asymmetric rotation. Such a transition is due to a decrease in the kinetic energy of rotation of the liquid during the formation of vortices moving with the reservoir.

The synchronism of vortex movement and rotation of the tank clearly follows from the practical coincidence of the period of current oscillations with the period of rotation of the tank. After the asymmetric rotation is established, the electrode does not significantly affect it.

Due to the dual role of the recording electrode, the indicated method allows to demonstrate previously unknown spin-laws, in particular, the stability of asymmetric rotation of a fluid in a symmetrical reservoir and the constancy of the radial velocity of the front of rotation during fluid braking.

The implementation of the recording electrode in the form of a tape, the insulated cantilever part of which serves as a current output, can reduce the slowdown of the flow by the electrode. The following circumstances contribute to this: 1) the radial location of the tape, reducing its path in a rotating fluid, 2) the possibility of reducing the thickness of the tape by increasing the width of the tape along the stream while maintaining the stiffness of the electrode, 3) the ability to perform the tape with the surface of the body of revolution, for example, with a conical and cylindrical surfaces, which increases rigidity at a given tape thickness, but does not increase hydrodynamic resistance due to the natural flow of such a surface with a rotating fluid.

The following notation is used in the drawings and in the text:

t is the time

φ is the azimuthal angle,

 Ω is the constant angular velocity of the tank after it is started,

V is the voltage of the source,

J is the total instantaneous current of the active plate,

J (φ) is the eddy current component,

- предельный ток активной пластины,

- limiting current of the active plate,

u is the velocity of the fluid in the flow in front of the plate (the indices of the current and velocity denote the values corresponding to each other),

u _φ is the total azimuthal (tangential) velocity of the liquid,

u _φo (φ) is the vortex component of the azimuthal velocity,

u _f is the radial velocity of the front of rotation of the liquid,

d _r is the diameter of the tank, spherical or cylindrical (also the number in an open circle and square, respectively),

T _r - the rotation period of the tank (the duration of one revolution, also the number under an open circle or square),

T is the period of current oscillations,

τ is the duration of the short stage of current oscillations (the interval between the nearest absolute extrema for the period),

Θ is the shortest angular distance between the axes of the opposite vortices in the equatorial plane of the tank,

F is a function that describes the form of current oscillations,

0.001 ... 0.25 M is the concentration of each of the reagents K ₃ Fe (CN) ₆ and K ₄ Fe (CN) ₆ in an aqueous solution containing an excess of KOH (100-fold for reagent concentrations of 0.001 ... 0.004 M);

λ _p - the length of the active part of the plate along the stream,

η _p - the total length of the partially insulated plate along the stream,

χ is the height of the active plate along the axis of rotation of the tank,

ε _p is the thickness of the active plate (0.1-0.2 mm),

δ _p - the distance of the active plate to the tank wall in the equatorial plane (accurate to the thickness of the plate),

δ _e is the actual thickness of the diffusion layer,

δ _i - theoretical value of the thickness of the diffusion layer,

δ _s is the limiting thickness of the diffusion layer with layering,

ν is the kinematic viscosity of the liquid,

ξ is the moment the tank stops before the current rises,

ϑ - delay in the rise of current after a pulsed start of rotation of the tank (the beginning is marked with a vertical dash),

κ (Greek) - the moment of slope of the current rise steepness,

w is the duration of the portion of the greatest steepness of the current rise,

↓ ↑ (separate arrows under the current curve) - moments, respectively, of stopping and starting the tank.

The drawings show:

Figure 1 - device for demonstrating vortex resonance during spinup. Figure 2 - section aa in figure 1 (rotated). Figure 3 - spherical tank with two recording electrodes. Figure 4 is a cylindrical tank with two recording electrodes. 5 is a symmetric system of two recording electrodes. 6 is a view B in figure 5. 7 is a recording electrode in the form of a tape with a flat active plate. Fig.8 is a view In Fig.7. Fig.9 - recording electrode with a cylindrical active plate. Figure 10 is a view of D in figure 9.

11 is a recording electrode on a cylindrical template. Fig.12 is a view of D in Fig.11. Fig - recording electrode on a conical pattern. Fig.14 is a view of E in Fig.13. Fig - fiber suspension of the recording electrode. Fig.16 is a view of G in Fig.15. 17 is a composite recording electrode. Fig. 18 is a recording electrode with a flat cantilever part in a perspective view. Fig. 19 is a recording electrode with a conical cantilever part in a perspective view. Fig - shift and rotation of the recording electrode in the tank with the formation of the angle of attack α relative to the flow.

Fig - active plate with isolation of one side and with rotation at an angle of attack to the flow. Fig - forms of the active plate with free and partially insulated surfaces (the insulated part of the plate is shaded, arrows are the possible flow directions).

Fig - types of pulses of rotation of the tank and the corresponding form of the dependence of the current of the recording electrode on time.

- напряжение V» при двух скоростях вращения резервуара (периоды 1.28 и 5.64 с); активная пластина размером 3×10×0.1 мм свободна от изоляции и работает двумя сторонами (площадь 0.6 см²).Fig - instant relief of the fluid rotation speed in the tank and its similarity to the shape of the current dependence in Fig.23 (points P ₁ , P ₂ , P ₃ , P ₄ in Fig.23 correspond to the moments of passage of the same points in Fig.24 past the electrode in the process of movement of the front of rotation of the liquid to the center of the tank). Fig - characteristics of the recording electrode "current limit

- voltage V "at two speeds of rotation of the tank (periods 1.28 and 5.64 s); the active plate 3 × 10 × 0.1 mm in size is free from insulation and works on two sides (area 0.6 cm ² ).

Fig. 26 is a diagram of a flow around an active plate and the formation of a diffusion layer with stationary thickening and non-stationary layering, which are caused by flow separation; the thickness of the diffusion layer: δ _i - classical, δ _e - actual, δ _s - with layering during the development of flow separation. 27 is a flow diagram of a partially insulated active plate.

28-35 are the observed forms of the periodic component of the current as a function of the azimuthal angle φ linearly increasing with time (expressed by the function Φ with the indicated values of the parameters k and f).

Fig.36-43 - sectors and axes of the associated (+) and counter (-) vortices in the equatorial plane of the tank according to the shape of the current in Figs. 28-35 (the boundaries of the sectors correspond to the zeros of the periodic component of the current, the axis of the associated vortices to the maxima, the axis of the counter vortices - lows).

Fig.44 is an oscillogram of the curve "current J - time t" when spinup in a spherical tank with a rotation period T _r = 1.32 s; in the upper part - the continuation of the current curve with the beginning of the sweep at time t = 115 s (time is set at the beginning of the sweep); This moment corresponds to the final stage of the spinup with almost complete damping of the current oscillations. Fig.45 is an oscillogram in the conditions of Fig.44, but with an increased rotation period T _r = 5.56 s.

Fig - waveform in the conditions of Fig with increasing distance δ _p between the recording electrode and the wall of the tank. Fig - waveforms of the current when spinup with a single (shown three sweeps) and multiple intermittent starting rotation of a spherical tank; under the intermittent start curve - arrows turn off ↓ and turn on ↑ engine, T _r = 5.56 s.

Fig.48-49 - the identification of the role of the initial fluid velocity at the time of starting the tank. Fig. 48 - initial velocity is zero; there are no current oscillations until the front of rotation arrives at the recording electrode (moment ϑ). Fig - initial linear velocity is 4% of the velocity of the wall of the tank; current oscillations, indicating the presence of vortices, occur immediately after start-up, before the front arrives at the recording electrode, which indicates the independence of the vortex formation mechanism from the electrode.

Fig. 50 shows a stepwise increase in current when a part of the reverse flow region is removed by a single shock of the active electrode plate (longitudinal displacement of 1 mm in less than 0.1 s, equal to the duration of the current jump). Fig - the process of establishing the maximum current when closing the circuit of the recording electrode during the rotation of the tank (upper part of the figure); An oscillogram of the current growth from the beginning of the start-up of the tank (the lower part of the figure) is also shown.

Fig - current to a partially insulated plate when changing the direction of rotation of the tank (the moment of the change of direction is shown by the down arrow ↓); the front is first the open part of the plate, then the insulated part (shaded). Fig - approximate correspondence of the times: 1) the delay of the current rise after starting the tank (kink of the curve below), 2) the delay of the current drop after stopping the tank (kink of the curve at the top, the moment the tank was stopped is indicated by the down arrow ↓).

Fig. 54 shows the effect of maintaining the radial velocity of the front of rotation of the liquid after the spherical reservoir stops prematurely at the moment ξ <ϑ; curve A ₁ - with a premature stop of the tank, curves A ₂ and A ₃ - without a premature stop, but with different initial fluid velocities. Fig - waveforms of current in a cylindrical tank with two recording electrodes remote from the wall of the tank at a distance of 6 and 10 mm; indices A and B at ϑ and δ _p relate these values to curves A and B, shifted vertically; at the top are the same curves on the second scan with the beginning at t = 13.7 s (the follow-up period of the sweeps is 14.6 s).

In the experiments, smooth nickel tapes with a thickness of 0.1 mm (Figs. 44-46, 48-51, 53) and 0.2 mm thick (Figs. 47, 52, 54, 55) were used. The thickness of the insulating film is 20 microns. The contour of the active electrode plate is shown on the oscillograms as a rectangle with the dimensions of the sides; the horizontal arrow in front of the circuit is the flow direction. The duration of establishing a constant angular velocity of the tank during pulse start-up is no more than 0.1 s. Load resistance 20 ohms. The voltage of the source is V = 0.25 V (it coincides with the voltage at the electrodes up to a relatively small ohmic drop). Temperature 20 ± 1 ° С.

A device for demonstrating vortex resonance during spinup (Fig. 1) includes a reservoir 1 with a spherical wall 2 and a vertical axis of symmetry 3. Wall 2 has a mark 4 for monitoring the angular position of the reservoir. The tank is made to rotate about a vertical axis of symmetry, which, thus, is simultaneously the axis of rotation 5 of the tank. In the tank is a liquid 6, which is an aqueous solution of a redox system. The composition of the solution:

0.002 M K ₃ Fe (CN) ₆ +0.002 M K ₄ Fe (CN) ₆ +0.2 M KOH.

The recording electrode 7 and the auxiliary electrode 8, which is superior in terms of active area, are immersed in the liquid. The electrodes are made of nickel and mounted on a stationary vertical rod 9, which is aligned with the axis of rotation of the tank (the axis of rotation passes through the cross section of the rod).

The recording electrode is an electrically conductive tape 10, which includes a console 11 in the role of the cantilever part of the tape and an active plate 12 in the role of the active part of the tape. The active plate is located symmetrically relative to the plane 13 passing through the axis of symmetry of the tank, and is oriented along this axis. The active plate is crossed by the equatorial plane 14 of the reservoir (horizontal level of the largest internal diameter).

The electrodes 7, 8 are connected to the opposite poles of the voltage source 15 V through an electric circuit 16 containing the load resistance 17. The recording electrode is the cathode (polarity "minus"), the auxiliary electrode is the anode (polarity "plus"). The ends of the load resistance are connected to the inputs of the oscillographic recorder 18, which amplifies the potential difference proportional to the current J in the circuit.

During the demonstration, oscillograms are obtained in the coordinates “current J of the recording electrode - time t”. The time starts when the tank starts t = 0.

After the pulse onset of rotation of the reservoir, two zones are formed in it, differing in the speed of rotation of the fluid around the axis of rotation 5: the inner zone 19 without rotation of the liquid and the outer zone 20 with rotation of the liquid. In the equatorial plane of the zone are separated by a line 21 of the front 22 of rotation. The front of rotation moves from the tank wall to its axis of symmetry. In addition to the movement characterized by azimuthal (or, equivalently, tangential) velocity, the fluid makes a movement in the meridian plane. Moreover, all movement of the untwisted fluid is symmetric about the axis of rotation of the tank. The moment of approach of the rotation front to the active plate is recorded as a sharp break in the current waveform at t = ϑ, separating the horizontal section from the steep rise.

The initial radial velocity of the front can be estimated from the oscillograms by the formula

u _f = δ _p / ϑ.

The approach of the rotation front to the active plate changes the type of symmetry of the fluid motion. The rotation of the liquid becomes asymmetric about the axis of rotation of the tank. Vortices 23, 24, 25, 26 with axes 27, 28, 29, 30 and boundaries 31, 32, 33, 34 are added to the symmetric component of rotation (in the drawing, the boundary is indicated by a dot in the form of a circle in a rectangle). Vortices 23, 25 are associated (marked with a plus sign). The fluid circulation in them coincides with the direction of rotation of the tank. The vortices 24, 26 are oncoming (marked with a minus sign). In the direction of circulation, they are opposite to the rotation of the tank. The intersection of the axis of the vortices with the equatorial plane of the reservoir defines the centers of the vortices (in the drawing, the centers of the vortices are circled in two circles).

Associated eddies increase the velocity of the flow incident on the active plate, which leads to an increase in current. Counter vortices, on the contrary, reduce current. For this reason, the appearance of vortices in the reservoir is displayed on the waveform by the occurrence of current oscillations (t ₀ , t ₁ , ..., t ₇ are the moments of passage of the axes and boundaries of the vortices through the symmetry plane 13 of the active plate 12).

Vortices exhibit a tendency to be fixed inside a rotating reservoir, which is equivalent to resonance with equal periods

T = T _r

where T is the period of current oscillations, measured as the time interval between similar in shape extrema (absolute minimums 35, 36 in figure 1),

T _r is the rotation period of the tank.

The existence of a fluid rotation front with a clear line 21 characterizes the main spinap stage. The duration of this stage is about 10 periods (revolutions) of the reservoir, during which the front manages to reach the axis of the reservoir. It is at the main stage of the spinup that the exact coincidence of the periods occurs.

Over time, the liquid approaches a state of solid-state rotation, in which all its regions have the same angular velocity. As this spinup completes, the vortex motion decays and the amplitude of the current oscillations tends to zero. At the final stage of the spinup, there is a limited increase in the period T of current fluctuations compared with the period T _{r of} rotation of the tank within 20% of T _r . A relatively small deviation of T from T _{r is} similar to resonance detuning.

The presence in the tank of a fixed rod with a relatively small diameter (less than 0.1 of the diameter of the tank) practically does not affect the process of unwinding of the liquid. However, placing a ball in the reservoir (not shown in the drawing) with a diameter of 0.3 from the diameter of the reservoir allows observing the spin stop at the stage of stationary differential rotation of the liquid, which is similar to the main spin stage (“frozen spin”).

Under these conditions, stationary equality of the period of current oscillations and the period of rotation of the reservoir (T = T _r ) with constant fixing of the vortices is achieved. In experiments with the ball, the exact equality of the periods can be observed indefinitely, over hundreds of revolutions of the tank.

In the described experiments with unsteady spinning of a liquid, the equality of periods occurs temporarily, at the main stage of the spin-up. However, the non-stationary process considered in the present invention helps to explain the origin of the vortices, including during stationary differential rotation. An essential argument for this explanation is the mismatch between the periods of current oscillations and the rotation of the reservoir at the final stage of the spin-up.

The fact that the vortices slip along the wall of the reservoir, resulting from the mismatch of the periods, excludes the trivial cause of the vortices in these experiments - Rossby waves, which can be caused by the asymmetric part of the reservoir (skewed bottom) and impose a constant orientation on the vortices relative to this part, i.e., they do not allow sliding.

The absence of this trivial reason confirms the deeper physical meaning of the resonance origin of the observed vortices, which is associated with a decrease in the kinetic energy of the liquid during the transition from symmetric to asymmetric rotation.

From the experiments it follows that fluid is involved in the vortex motion on both sides of the front of rotation, which accelerates the transfer of rotation to the central region of the reservoir. In this case, the front line of rotation divides each vortex into two parts — the outer part 37 and the inner part 38. Vortices deform the front during its movement.

The swirl velocity of the fluid includes the azimuthal and radial components. On the axis of the vortices, both velocity components are equal to zero. At the boundaries between the vortices, the azimuthal component vanishes.

The circulation of the associated vortex is superior in maximum linear velocity to the circulation of the oncoming vortex. Correspondingly, the region occupied by the associated vortex is larger than the region of the oncoming vortex, which is an additional factor in the axial asymmetry of the fluid flow in the reservoir.

In addition, in the general case, the position of the centers of opposite vortices is also asymmetric with respect to the axis of rotation, which is expressed in the asymmetry of the current change over one period of oscillations, that is, in the unequal rise and fall times. The short phase of the period can be a fall or rise in current. In this case, the shortest angular distance Θ between the centers of the vortices is less than 180 ° and is

Θ = 2πτ / T,

τ is the duration of the short stage of the current oscillation period, τ <T / 2.

The contour of each vortex is approximately transmitted by a closed current line passing through a point with a maximum circulation speed.

The tape console is covered with an insulating film 39 to the border 40 with the active plate. The insulating film contains chloroprene rubber with a polymer chain of -CClCHCH ₂ CH ₂ - units, which makes it stable in an alkaline environment.

The inner end 41 of the console is bonded to the rod 9. The outer end 42 of the console, remote from the rod, has a longitudinal bend 43 and is adjacent to the active plate 12.

The tank is mounted on a lower horizontal pulley 44 made of vinyl plastic and coated with a rubber gasket 45. The lower pulley rests on the outer ring 46 of the ball bearing 47. The inner ring 48 of the ball bearing is mounted on a fixed vertical axis 49.

The side surface 50 of the lower pulley is in frictional contact with the drive pulley 51, mounted on the shaft 52 of the reversible electric motor (the motor is not shown in the drawing). By turning the motor on and off, respectively, pulse start and pulse stop of rotation of the tank are achieved.

The lower pulley has a groove 53 for a belt drive. The tank has a neck 54. In the middle height portion of the neck is the level 55 of the free surface 56 of the liquid. A cap 57 with an opening 58 for the rod 9 is mounted on the neck.

The rod passes through the sleeve 59, mounted in the plate 60, which lies on the supports 61, 62 and has the ability to move horizontally with subsequent fixation. An upper horizontal pulley 63 with a groove 64 for belt transmission is dressed on the upper end of the rod (grooves 53 and 64 are redundant and are not used in the main version of the device).

A collector 65 of three mutually insulated brass rings 66, 67, 68 with sliders 69, 70, 71 is mounted above the upper pulley on the shaft for electrical contact with two recording electrodes and one auxiliary electrode. In the simplest case, one recording electrode is used (as shown in FIG. 2).

Possible options for the operation of the device with two recording electrodes in a spherical (figure 3) or cylindrical (figure 4) tanks. The recording electrodes 72, 73 are located symmetrically with respect to the axis of rotation 74 of the spherical tank 75. Similarly, in the cylindrical tank 76 with the axis of rotation 77, the recording electrodes 78, 79 are located.

In the cylindrical tank, height-adjustable horizontal partitions 80, 81 are installed. The lower partition 80 with three screws 82 rests on the bottom 83 of the tank. The upper partition 81 is suspended on the cover 84 using three studs 85 secured by nuts 86.

Symmetric recording electrodes 72, 73 are mounted on a polymer rod 87, which enters the nickel tube 88, which serves as an auxiliary electrode, and is fixed with rubber inserts 89, 90. For introducing symmetrical recording electrodes into a spherical vessel through the neck, it is possible to temporarily bend the tapes 91, 92 of the electrodes to positions 93, 94 (Figs. 5, 6).

The implementation of the recording electrode allows a number of options.

The simplest option (Fig. 7, 8), in which the recording electrode 95 in the form of a tape 96 is made of a straight sheet blank by bending it twice to form three flat sections 97, 98, 99 directed at right angles to each other, or flat sections 97, 100, 101 with obtuse angles between them.

The insulating film 102 covers sections 97, 98 and the upper part of section 99 to the boundary 103 with the active plate 104. The tape section 97 is bonded to a face 105 of the vertical rod 106. The rod has a square cross section and a symmetry axis 107 aligned with the axis of symmetry of the tank. In this embodiment, the tape 96 is symmetrical about a plane 108 passing through the axis of rotation 109 of the tank. The auxiliary electrode 110 in the form of a curved plate 111 is bonded to the other face 112 of the rod.

In another embodiment (FIGS. 9, 10), the recording electrode 113 based on the tape 114 includes elements that are part of the body of revolution. In this case, such elements are the active plate 115 and the mounting section 116 having cylindrical surfaces 117, 118.

The recording electrode 113 and the auxiliary electrode 119 are mounted on a vertical rod 120 of circular cross section. The recording electrodes with surfaces of revolution can be made by bending sheet blanks on templates, in particular, a continuous workpiece 121 on a cylindrical template 122 (Fig. 11, 12) and a workpiece 123 with an opening 124 on a conical template 125 (Fig. 13, 14).

The stiffness of the tape 126 of the recording electrode 127 can be increased with the help of fiber 128, which in the form of a loop 129 bends around the end 130 of the console 131 and the vertical rod 132 (Fig. 15, 16). On the rod, the loop is fixed by stops 133, 134. A decrease in the thickness of the active plate 135 without a significant reduction in the stiffness of the recording electrode can be achieved by welding the tape 136 from sheets 137, 138 differing in thickness (Fig. 17).

The symmetry of the tape 139 with the active plate 140 relative to the plane 141 passing through the axis 142 of rotation of the tank, helps to reduce the hydrodynamic resistance of the recording electrode 143 to the fluid flow (Fig. 18). The conical surface 144 of the tape 145 is oriented along the flow lines of a freely rotating liquid, which allows to increase the rigidity of the recording electrode 146 without distorting the shape of the stream (Fig. 19).

For a controlled influence on the flow shape, the active plate 147 of the recording electrode 148 can be rotated at a given angle α (angle of attack) to the direction of flow, which is ensured by the displacement of the vertical rod 149 from the axis of rotation 150 of the reservoir 151 (Fig. 20). With this arrangement of the active plate, one side 152 and the edges 153, 154 can be covered with an insulating film 155 (Fig.21).

In addition, an insulating film can be deposited on the active plate 156 in the form of strips 157, 158, 159 having different widths and oriented transversely to the flow (Fig. 22, the flow direction is shown by arrows, λ _p is the length of the part of the active plate free of insulation, η _p is the total length of the active plate along the flow, η _p > λ _p ). In this case, the parts of the plate 160, 161 that are located respectively at its leading edge 162 and trailing edge 163 remain open. At the same position of the partially insulated plate, the role of the edges can be changed by changing the direction of rotation of the tank.

In the described method, three types of impulse dependence of the angular velocity Ω of the reservoir on time t with a start at t = 0 are used (Fig. 23): impulse Ω _{1 of} unlimited duration; a pulse Ω ₂ with a duration ξ less than the time ϑ of the arrival of the front of rotation of the liquid to the recording electrode; a sequence of Ω ₃ periodically repeating pulses.

Comparison of the current waveforms obtained with pulses Ω ₁ and Ω ₂ shows the independence of the time ϑ of the arrival of the front of rotation of the liquid from the duration of the pulse of rotation of the tank. The unusual nature of this effect makes it an interesting object for a visual demonstration. The shape of the monotonous dependence of current on time gives a picture of the radial profile of the fluid velocity in the process of its unwinding (Fig.24).

With a negative polarity of the recording electrode (cathode), the current is due to the electrochemical reduction reaction

Fe (CN) ₆ ^3- + e↔Fe (CN) ₆ ^4-

on the surface of the active plate. The current strength J depends on the voltage V at the recording and auxiliary electrodes, as well as on the rate of ion delivery through the diffusion layer, the thickness of which decreases with an increase in the flow velocity incident on the active plate. At a fixed flow velocity, the thickness of the diffusion layer increases with distance from the leading edge of the active plate, and the current density, as a consequence, decreases.

, зависящий от скорости и жидкости и, соответственно, от периода Т_r вращения резервуара (фиг.25).A voltage of V> 0.2 V is sufficient to recharge almost all the ions that have approached the electrode surface. A further increase in voltage ceases to affect the reaction rate. At V = const, the limiting current is reached

depending on the speed and fluid and, accordingly, on the period T _{r of} rotation of the tank (Fig.25).

с точностью 1% от его истинного значения необходимо время, которое согласно приведенным осциллограммам эквивалентно нескольким оборотам резервуара (приблизительно шести оборотам с периодом 1.5 с).To set the current limit

with an accuracy of 1% of its true value, a time is required which, according to the given oscillograms, is equivalent to several tank revolutions (approximately six revolutions with a period of 1.5 s).

устанавливается за десятую долю оборота, что делает возможным приближенное измерение колебаний скорости жидкости путем регистрации колебаний мгновенного тока.With an accuracy of 20% current

is set for a tenth of a revolution, which makes it possible to approximate the measurement of fluid velocity fluctuations by recording the instantaneous current oscillations.

In the experiments described, when flowing around a plate, the Reynolds number is

Re _p = π (d _r -2δ _p ) λ _p / νT _r ,

where ν is the kinematic viscosity of the liquid. The condition for laminar flow around a smooth plate is Re _p <3000.

The experiments of Fig. 25 correspond to the values: d _r = 12.7 cm, δ _p = 0.8 cm, λ _p = 0.3 cm, T _r = 1.28 s and 5.64 s, ν = 0.01 cm ² · s ^-1 . Moreover, max Re _p = 817, that is, the flow around is laminar.

от скорости набегающего потока u,

(Левич В.Г. Физико-химическая гидродинамика, Москва, 1959, с.98), илиThe classical theory of laminar flow around a plate leads to a quadratic dependence of the limiting current

on the speed of the oncoming flow u,

(Levich V.G. Physico-chemical hydrodynamics, Moscow, 1959, p. 98), or

where u ₁ , u ₂ are two values of the flow velocity in front of the plate,

,

- соответствующие значения предельного тока на пластину.

,

- the corresponding values of the limiting current to the plate.

The spin-up experiments show a significant deviation from the quadratic dependence. For example, with the length of the active plate λ _p = 3 mm (according to Fig.25)

From similar measurements with active plates of other sizes, it follows that in the formula

exponent n substantially depends on the length λ _{p of the} active plate, n = n (λ _p ). The following values can be recommended for calculations: n = 2.4 ± 0.1 at λ _p = 6 mm, n = 2.7 ± 0.1 at λ _p = 3 mm.

When registering the oscillations of the instantaneous current J, the approximate equality

u ₂ / u ₁ ≈ (J ₂ / J ₁ ) ⁿ ,

where J ₁ and J ₂ are the instantaneous currents corresponding to the flow velocities u ₁ and u ₂ in front of the plate. This implies the expression for the amplitudes Δ of the current J and the flow velocity u:

Δu / u≈nΔJ / J.

Thus, under the conditions of the described experiments, the relative amplitude of the flow velocity is 2.4 ... 2.7 times greater than the observed relative amplitude of the current. The relative range of 2Δu / u of velocity fluctuations caused by the formation of vortices reaches 25% of the average flow rate at a fixed point in the tank.

A significant increase in the exponent n compared with the classical value of 2 indicates a thickening of the diffusion layer caused by flow separation and the formation of a backflow region 164 near the leading edge 165 of the active plate 166 (Fig. 26). The true diffusion layer 167 (thickness δ _e ) is thicker than the classical diffusion layer 168 (thickness δ _i ) and exhibits a tendency to gradually thicken with the formation of stationary layering 169 (additional layer to the total thickness δ _s ) for a period of about 10 minutes.

Layering can be destroyed by light shaking of the electrode. In this case, the diffusion layer 167 is abruptly restored, after which the thickening process is resumed and layering is formed during the same exposure. The braking of the liquid without a complete stop and repeated unwinding to the previous speed restore stationary layering without holding, that is, almost instantly. To reproduce the shutter speed, a complete stop of the fluid is necessary before re-spinning.

The application of an insulating layer 170 to a surface portion 171 adjacent to the leading edge 172 of the plate 173 (FIG. 27) reduces the thickness of the true diffusion layer 174 on the insulating part of the plate, however, with a plate length of up to 10 mm, this decrease is insignificant and the exponent continues to exceed theoretical value n = 2.

On the oscillograms obtained by the described method, periodic current oscillations are clearly distinguished against the background of its monotonically increasing average value. To analyze the shape of the observed oscillations, the average current value must be taken as the reference point of the periodic component J (φ) of the current (Fig. 28-35). In this case, the shape of the current oscillations allows us to judge the relative position of the liquid vortices in a rotating reservoir (Figs. 36-43).

An independent variable is time t or the azimuthal angle φ associated with time by the relation

φ = Ωt + const,

where Ω is the angular velocity of the tank. Under conditions of vortex resonance, that is, at T = T _r , the period T of the current oscillations corresponds to the period 2π of the azimuthal angle.

The current oscillation period is defined as the minimum interval of time t or the azimuthal angle φ between extrema of similar shape, for example, between maxima of 175, 176 or between minima of 177, 178, which are similar in shape because they are absolute for one period, in contrast to relative maxima 179 and a minimum of 180 (FIG. 28).

The observed forms of the periodic component of the current can be described by the expression

F = sinφ + fsin (2φ-kπ / 2)

with parameters f and k, taking different values (Fig.28-32).

The periodic component of the current has the following characteristic points within the period: zeros 181, 182, 183, 184, maxima 185, 186, minima 187, 188 (Fig. 28).

In a first approximation, the difference in the circulation speeds of the associated and oncoming vortices is permissible not to be taken into account. In the equatorial plane of the spherical reservoir, up to the indicated difference, the current zeros correspond to the boundaries 189, 190, 191, 192 between the sectors of the vortices, the current maxima correspond to the axes 193, 194 of the associated vortices, the current minima correspond to the axes 195, 196 of the opposing vortices (Fig. 36), moreover, at the intersection with the equatorial plane, the axis of the vortex is equivalent to the center of the vortex. Similarly, the correspondence between other forms of currents (Figs. 29-35) and eddy parameters (Figs. 37-43).

The superiority of the associated vortex over the counter in terms of circulation speed leads to a displacement of the boundaries to the positions 197, 198, 199, 200, which reduce the sectors of the counter vortices and are schematically shown with a dashed line (Figs. 38, 39).

In cases of merging current extremes (Figs. 34, 35), in the equatorial plane between the centers of the opposing vortex 201, 202, a line 203 of zero azimuthal eddy circulation velocity is formed (Fig. 42), and a similar line 206 is formed between the centers of the associated eddy 204, 205 (Fig. 34). .43).

Examples of the demonstration of vortex resonance and its attendant phenomena are shown in the given oscillograms (Figs. 44-55). All waveforms contain a kink marking the time ϑ of the arrival of the front of rotation of the liquid to the electrode, which allows you to determine the initial velocity of the front of rotation.

The comparison of Fig. 44 with Fig. 45 shows a proportional increase in the period of current oscillations with the period of rotation of the tank. In Fig. 45, the current oscillation period is T = 5.7 s, the current rise time is τ = 1.9 s, the current decay time is T-τ = 3.8 s, and the angular distance between the vortex axes is Θ = 2πτ / T = 2π / 3 = 120 °.

A comparison of FIG. 44 with FIG. 46, and FIG. 45 with FIG. 47 shows an increase in the time ϑ of arrival of the front of rotation with increasing distance δ _{p of the} active plate to the tank wall. From Fig. 47, in addition, it follows that periodic starting and stopping the rotation of the tank at equal time intervals (5 s) are accompanied by unequal durations of ups and downs of current: the rise is twice as fast.

According to Fig. 48, in a spherical tank with an inner diameter d _r = 127 mm, a rotation period T _r = 1.55 s, a wall distance to the active electrode plate δ _p = 8 mm, the approach time of the front of rotation of the liquid to the plate is ϑ = 1.38 s, whence the initial the speed of the radial motion of the front of rotation of the liquid is

u _f = 0.8 cm / 1.38 s = 0.58 cm / s.

Under the same conditions, the period of current oscillations is T = 1.55 s (Figs. 48, 49), which coincides with the rotation period of the tank and corresponds to an exact eddy resonance,

T = T _r = 1.55 s.

The exact vortex resonance is practically achieved in the experiments of Figures 50-52 at the main stage of the spin:

T = T _r = 1.28 s (Figs. 50, 51),

T = T _r = 1.34 s (Fig. 52).

In a number of the above experiments, a tendency of the period of oscillations to a gradual increase is visible: 1.4 s≤T≤1.6 s at T _r = 1.32 s (in Figs. 44, 46), T = 5.7 s at T _r = 5.56 s (in Fig. 45) , 1.34 s≤T≤1.36 s (in FIG. 52).

The oscillograms of Figs. 48, 49 were obtained under the same conditions, except for the velocity of the liquid at the time of the start-up of the tank. In Fig.48, the liquid is stationary, in Fig.49 rotates by inertia after the previous rotation and stopping of the tank. The initial azimuthal velocity u _φ of fluid rotation at the location of the active plate can be estimated from the ratio of currents on the waveform of FIG. 49:

J (t = 0) /maxJ=0.29,

u _φ (t = 0) / max u _φ = (0.29) ^2.7 = 0.035,

where the symbols "t = 0" and "max" indicate, respectively, the initial and maximum values of current J and azimuthal velocity u _φ . Within the waveform, the maximum speed can be estimated

max u _φ ≈π (d _r -2δ _p ) / T _r = 22.5 cm · s ^-1 ,

since d _r = 12.7 cm, δ _p = 0.8 cm, T _r = 1.55 s.

From here

u _φ (t = 0) ≈0.79 cm s ^-1 .

With such a relatively low initial liquid velocity, vortices arise immediately after the rotation of the reservoir begins, before the rotation front arrives at the recording electrode.

This is evidenced by current fluctuations in the time interval t from 0 to ϑ (Fig. 49), in contrast to the experiment with the original stationary fluid, where there are no such oscillations (Fig. 48).

In this experiment, the vortices recorded by the electrode are formed practically without its participation and, therefore, are an asymmetric form of free rotation of the liquid. This gives additional reasons to consider the vortex resonance, observed under more general conditions, as a universal property of a fluid rotating in a reservoir of ideal shape.

At a sufficient speed, the free motion of such a liquid has two states - symmetric and asymmetric, which can transform into each other with minor external influences. In the described experiments, the source of such an effect is a recording electrode.

In the series of experiments of Figs. 50, 51, the demonstration of vortex resonance simultaneously reveals the features of the hydrodynamic flow around the plate, leading to an abnormal increase in the exponent n in the ratio between current and fluid velocity.

The stepwise increase in current in Fig. 50, caused by shaking of the electrode, indicates the removal of part of the boundary layer (referred to as layering here and in Fig. 26), as well as the separation of the flow near the leading edge of the plate.

The reverse flow associated with the separation leads to a swelling of the boundary layer and, as a result, to a slowdown in the delivery of the reacting substance to the electrode. The presence of the reverse flow region also slows down the updating of the boundary layer on the active plate when it is surrounded by a fluid flow.

The update rate of the boundary and diffusion layers is characterized by the current decay time to the limiting value after the electrode circuit is closed during rotation of the tank (upper L-shaped curves in Fig. 51). According to the waveform, the decay time is approximately six periods of current fluctuations, which corresponds to six turns of the tank. Thus, in order to update the boundary layer, the active electrode plate must travel a distance 800 times greater than the plate length in the liquid.

The waveform of Fig. 52 is taken on a partially insulated plate with a total length along the flow η _p = 6.5 mm and an open strip length λ _p = 2 mm at the edge of the plate. First, the open strip is located in front of the plate with respect to the fluid flow, then in the back of the plate. The change in position of the open strip is achieved by changing the direction of rotation of the tank. In the forward position of the open strip, the limiting current is 1.22 times higher than in the rear, due to an increase in the thickness of the boundary layer along the plate. The shape and period of current oscillations are the same in both directions of rotation.

On the oscillogram of Fig. 53, the length w of the steepest rise in current after the arrival of the rotation front to the active plate is highlighted and the current decreases after the tank stops (the stopping moment is shown by the arrow ↓).

In Fig. 54, the delay ϑ of the start of the current rise is the same for three curves obtained for different rotation modes of the spherical tank (from the bottom up): A ₁ - premature stop of the tank at the moment ξ = 1.2 s before the start of the current rise at ϑ = 2.5 s (ξ≈ 0.5ϑ), A ₂ - restart the tank after 2 minutes without stopping the tank prematurely (displacement of the initial current level is the result of a weakened initial rotation of the liquid remaining after the previous start), A ₃ - the next restart after 10 s after the previous normal stop of the tank ( significant but the initial rotation of the fluid).

On Fig the front of rotation of the liquid sequentially approaches two recording electrodes located at different distances from the wall of the cylindrical tank, δ _pA = 6 mm and δ _pB = 10 mm; a comparison with the values of ϑ and T _r in Fig. 54 shows that when the cylindrical vessel is rotated twice as fast, the fluid rotation front in it moves at the same speed as in the spherical vessel. It follows that, ceteris paribus, the front of fluid rotation in a spherical vessel moves faster than in a cylindrical one.

The current fluctuations observed in the described experiments make it possible to construct an analytical expression for the vortex motion of a liquid in the equatorial plane of a spherical reservoir. Substitution of this expression into the stationary equation of the vortex in a rotating coordinate system makes this equation identical for two values of the maximum speed of the vortex motion: equal to zero and equal to approximately a tenth of the linear velocity of the reservoir.

It follows that the equation of a viscous incompressible rotating fluid allows for the simultaneous existence of two stationary solutions in a rotating coordinate system: symmetric and asymmetric with respect to the axis of rotation of the tank.

This is consistent with the results of the described experiments, which reveal the vortex attraction to a stationary position in a rotating reservoir, which is expressed in the coincidence of the current oscillation period and the rotation period of the reservoir.

The phenomenon of vortex resonance is essential for planetary physics. Under Earth's conditions, it means the possibility of localizing melt vortices under certain sections of the mantle. Providing accelerated heat removal from the liquid core, these areas become sources of plumes penetrating the mantle and activating volcanism. Deviations of the inner surface of the mantle from the ideal form increase the stability of vortex localization.

Claims (22)

1. A method of demonstrating vortex resonance in spinup, characterized in that the redox system is dissolved in a liquid, the liquid is poured into a tank having the shape of a body of revolution with a vertical axis of symmetry, the recording electrode and an auxiliary electrode exceeding it in active area are immersed, connected these electrodes to opposite poles of the DC voltage source, fix the recording electrode independently of the tank, make a pulse start of the tank in rotation with a constant angular velocity, measure the electric current through the recording electrode as a function of time, the beginning of the rise of the current is used as a sign of the arrival of the front of rotation of the liquid from the tank wall to the location of the active part of the recording electrode, measure the delay time of the rise of the current after the start of rotation of the tank, according to the measured delay time judge the radial velocity of the front of rotation of the liquid, a violation of the monotonicity of the growth of current with time, having the form of current oscillations, is presented as a sign of axial symmetries of the flow due to the formation of oppositely directed vortices, the axes of which outstrip the rotation of the liquid, compare the period of current oscillations with the period of rotation of the reservoir, and the coincidence of these periods is interpreted as resonance with the localization of the vortices in the coordinate system rotating with the reservoir. 2. The method according to claim 1, characterized in that the period of current fluctuations is measured as the minimum time interval between similar current extrema, and the limitation of their difference from above is considered to be a sign of coincidence of the period of current fluctuations with the rotation period of the tank, which is 20% of the rotation period reservoir. 3. The method according to claim 2, characterized in that the number of vortices in the horizontal plane passing through the active part of the electrode is determined by the number of current extrema for one oscillation period, and the direction of fluid circulation in the vortex relative to the rotation of the tank is determined by the type of extremum, and the maximum and the minimum current correspond to the associated and counter vortices. 4. The method according to claim 3, characterized in that the relative position of the axis of the vortices in a horizontal plane passing through the active part of the electrode is determined by the ratio of the duration of the rise and fall of the current between the extrema. 5. The method according to claim 1, characterized in that they use a tank with a spherical wall, while the active part of the recording electrode is placed at the level of the largest horizontal section of the tank in diameter. 6. The method according to claim 1, characterized in that the active part of the recording electrode is made in the form of a plate with a flat or cylindrical surface and orient this plate parallel to the axis of symmetry of the tank. 7. The method according to claim 1, characterized in that the rotation of the tank is carried out sequentially in two opposite directions. 8. The method according to claim 1, characterized in that a cylindrical tank with height-adjustable internal partitions is used, and a recording electrode is placed between the partitions. 9. The method according to claim 1, characterized in that the rotation of the tank is stopped before the current rises, the measured current delay time is compared with the current delay time measured during the rotation of the tank, and based on the coincidence of the measured delay times, it is concluded that independence of the radial velocity of the front of rotation of the fluid from the azimuthal velocity of the fluid after stopping the rotation of the tank. 10. The method according to claim 1, characterized in that before the pulse start of the tank, the liquid is informed of the initial rotation. 11. The method according to claim 1, characterized in that the circuit of the recording electrode is opened and closed during the rotation of the tank. 12. The method according to claim 6, characterized in that the plates of different lengths are used, they are oriented along the flow, the steady-state values of the limiting currents are measured during rotation of the tank with two periods providing laminar flow around the plates, and the exponent is calculated in the equality

where T _r1 , T _r2 - periods of rotation of the tank;

,

- corresponding limiting currents; n is an exponent, based on the calculation, it is shown that the exponent exceeds 2 and increases with decreasing plate length along the flow, which is associated with a thickening of the boundary layer on the plate due to the formation of a flow separation region. 13. The method according to p. 12, characterized in that in the case of a monotonic decrease in the limiting current with time, the electrode is displaced by the pulse with a return to its original position and the step of raising the limiting current is observed, which is associated with a reduction in the region of separation of the flow on the plate. 14. The method according to claim 1, characterized in that the intervals of rotation of the tank with constant angular velocity are periodically alternated with equal intervals of immobility of the tank, the duration of the rise and fall of the current between steady-state extreme values is compared by the current versus time, and shown in such a way that Under the conditions of the indicated intermittent rotation of the tank, a rise in current and, accordingly, an increase in the fluid velocity occur faster than the decline of these quantities. 15. The method according to claim 1, characterized in that the recording electrode is fixed with the possibility of rotation relative to the axis of symmetry of the tank. 16. The method according to claim 1, characterized in that the second recording electrode is immersed in the liquid and the currents through both recording electrodes are measured simultaneously. 17. A recording electrode for demonstrating spinap, characterized in that it is made in the form of an electrically conductive tape placed in a tank with liquid, along the length of the tape has a cantilever and active parts immersed in the liquid, the cantilever part is covered with an insulating film, one of the ends of the cantilever part is fastened with a vertical rod with the possibility of combining the rod with the axis of rotation of the tank and with the possibility of rotation of the rod, the end of the cantilever part remote from the rod has a longitudinal bend and is adjacent to the active part, which Luciano plate oriented along the axis of rotation of the tank. 18. The recording electrode according to 17, characterized in that the tape is symmetrical with respect to the plane passing through the axis of rotation of the tank. 19. The recording electrode according to 17, characterized in that the tape includes elements that are part of the body of revolution. 20. The recording electrode according to 17, characterized in that the plate is flat with the possibility of applying strips of insulating coating to the plate, as well as with the possibility of complete isolation of one of the sides of the plate. 21. The recording electrode according to claim 17, characterized in that the end of the cantilever portion of the tape remote from the rod is connected to the rod by a fiber loop. 22. The recording electrode according to claim 17, characterized in that the insulating film covering the cantilever portion comprises chloroprene rubber.

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