RU2543204C2 - Liquid mixing method - Google Patents

Abstract

FIELD: technological processes.

SUBSTANCE: invention relates to general-purpose mixing methods to implement different physical, chemical and hydrochemical (dispersion, emulsification, homogenisation, foam formation, destruction) processes with liquids and can be implemented in mixers of a different type with rotating mixing devices in fixed containers. Mixtures by means of a rotor with perforated discs simultaneously set the rotation with pulsations of speed and radial-axial oscillations, with that, swirled opposite submerged jets are shaped and length of their movement path is increased at volumetric circulation of these jets; besides, parameters of these movements of liquid are controlled as per a mathematical relationship.

EFFECT: invention provides for improvement of mixing efficiency due to deepening of turbulation by increasing circulation of flows and excluding stagnant zones and by increase of interaction of opposite internal submerged liquid jets.

1 tbl, 14 dwg

Description

The invention relates to general-purpose mixing methods for the implementation of various physical, chemical and hydromechanical (dispersion, emulsification, homogenization, foaming, destruction) processes with liquids and can be implemented in various types of mixers with rotating mixing devices in fixed tanks.

There is a method of centrifugal mixing of a liquid by means of a centrifugal homogenizer (AS USSR No. 554846, A01j 11/16), in which liquids by means of a rotating working body impart movement in either tangential or radial direction, creating its circulation in the region of rotation of the working body.

The disadvantage of this method is the low intensity of mixing, since the circumferential fluid flow prevails, and stagnant zones take place.

Known cavitation method of mixing fluid, implemented in a rotary pulsation apparatus (AS USSR 725691. Rotary pulsation apparatus.), Which consists in creating a forced pulsation of the fluid and cavitation, which gives rise to its hydrodynamic disturbances.

The disadvantages of this method is that when mixing biologically useful liquids, for example, emulsions for ice cream, due to the collapse of cavitation bubbles, the usefulness of the liquid properties is lost and a devastating effect is made on the biological component of the product.

Known vibration method of mixing, implemented in devices of vibration mixers (Utility Model Certificate RU No. 28988 U1 and Yatsun S.F. Extraction process under vibration exposure / S.F. Yatsun, V.Ya. Mishchenko, E.V. Artemenko // Vibration machines and technologies. - Kursk: KSTU Publishing House, 2003 - 280 p.), In which fluids force oscillating movements in the axial direction, while they are informed of linear accelerations, creating many flooded turbulent jets.

The disadvantage of this method, taken as a prototype, is that such actions on the object lead to the formation of stagnant zones around the axis of the working body and the restriction of fluid turbulization, which ultimately leads to a decrease in the intensity of mixing.

The problem to which the invention is directed is to increase mixing efficiency by increasing turbulization by increasing flow circulation and eliminating stagnant zones by communicating joint rotation and radial-axial vibrations to the working medium. And this, ultimately, will increase the interaction of oncoming internal flooded jets of liquid.

To solve this problem, a method for mixing liquid components is proposed, in which the mixture is forced, by means of a rotor with perforated disks, to simultaneously set rotation with velocity pulsations ± ε and radial-axial vibrations, at the same time, they form swirling counter-flooded jets and increase the length of their mixing path when volumetric circulation of these jets, and the parameters of these fluid motions are controlled according to:

where r, t, z are cylindrical coordinates;

ν is the kinematic viscosity coefficient;

p is the pressure;

ρ is the density of the liquid medium;

- амплитуда радиальных колебаний (в зоне диска);

- the amplitude of radial vibrations (in the area of the disk);

- амплитуда осевых колебаний (в зоне диска),

- the amplitude of the axial vibrations (in the area of the disk),

ω is the oscillation frequency of the rotor with disks;

R ₁ is the radius of the rotor disk;

R is the radius of the circle described by the oscillation drive;

D _d - the diameter of the disk;

l - departure of the rotatable body;

l ₁ - the distance between the disk and the drive of its vibrations;

D is the diameter of the circle described by the oscillation drive;

ω _BP - the rotational speed of the rotor with the disks, while the amplitude of the oscillations of the rotor with the disks is

and the frequency of its oscillations ω is determined depending on the type of mechanism used to create oscillations. For example, when using a device with an inertial vibration actuator to implement the claimed method, the oscillation frequency is determined by the formula:

where R ₁ is the radius of the rotor disk;

R is the radius of the rotor plate (the radius of the circle described by the oscillation drive);

D _d - the diameter of the disk;

l - departure of the rotatable body;

l ₁ - the distance between the rotor plate and the disk,

m is the reduced mass of the rotated body;

j is the stiffness of the rotor (when the rotor is hinged j = 0);

D is the diameter of the rotated body in the area of its interface with the counterbody;

P _oc - axial pressing force to the rotor counterbody;

ω _BP - rotor speed with discs for an eccentric or cam mechanism:

Comparison of the claimed method of mixing liquids with the known allows us to conclude that a new effect has been achieved, expressed in the possibility of increasing the length of their mixing path. This became possible due to the creation of swirling counter-flooded jets of liquid, which form due to the fact that the mixtures specify rotation with velocity pulsations and radial-axial vibrations. Moreover, changing the parameters of these movements according to the dependence proposed above, they control the step of the spiral trajectories of the swirling oncoming flooded jets, and hence the intensity of their interaction. In this regard, we can conclude that the criterion of "inventive step".

The invention is illustrated by drawings, where:

in FIG. 1 shows a diagram of the formation of swirling internal flooded jets;

in FIG. 2 shows a diagram of the interaction of internal flooded swirling jets with mixing with velocity pulsations and radial-axial vibrations (side view);

figure 3 shows a diagram of the interaction of internal flooded swirling jets with stirring with velocity pulsations and radial-axial vibrations (top view);

in FIG. 4 is a diagram for explaining the formation of fluid flows near a planar rotating disk;

in FIG. 5 shows the kinematic calculation scheme for determining the maximum speed (point A) on the periphery of the rotor disk;

in FIG. 6 shows a diagram of the implementation of the physical effect of fluidization of a liquid medium (turbulent mode);

in FIG. 7 shows a diagram of the implementation of the vibro-jet effect;

in FIG. 8 shows a diagram of the implementation of the effect of vibrational rotation support;

in FIG. 9 visually shows the initial moment of occurrence of the turbulent regime (for 0.5 sec);

in FIG. 10 visually shows the increase in the zone of turbulence in the working medium (for 1 sec);

in FIG. 11 shows the formation of ring waves illustrating the interaction of internal flooded jets;

in FIG. 12 visually shows the process of transition from laminar to turbulent mode of fluid motion with stirring;

in FIG. 13 shows a steady state mixing process;

in FIG. 14 shows the resulting water-oil emulsion at the end of the mixing process (5 min).

To implement the new principle of mixing, it is proposed to use a method in which a rotatable body with disks perforated by counter conical holes with the end surface is mated with a counterbody with a calibrated pressing force and is run along a closed path with rotational symmetry around the axis of symmetry of the path. This creates a circulation of counter flooded swirling flows of the working medium by informing it of joint rotation with pulsations of speed, radial-axial vibrations and increase the length of their mixing path. By changing the parameters of these forced movements, it is possible to control the trajectories of the counter swirling flows of the working fluid, which obviously makes it possible to control the intensity of the fluid mixing process, enhancing either the radial component or the axial component of the speed of movement of the flooded jets (Fig. 1). At the same time, by changing the angle of inclination α (Fig. 2) of the resulting velocities in the radial and axial directions, the pitch of the spiral paths of the swirling oncoming flooded jets changes, which means the frequency of interaction of the latter (Fig. 2, Fig. 3).

To clarify the essence of the method, we first consider the flow of a liquid medium near a flat disk (Fig. 4), uniformly rotating with an angular velocity ω about an axis perpendicular to the plane of the disk. Liquid away from the disc is taken at rest. Due to friction, the liquid layer immediately adjacent to the disk is carried away by the latter and, under the action of centrifugal force, is thrown outward from the disk. Instead of the discarded fluid, a new fluid flows to the disk in the axial direction, which is also carried away by the disc and is again thrown out. Therefore, in this case we have a completely three-dimensional flow. Moreover, due to the axial symmetry of the flow [G. Schlichting Theory of the boundary layer / G. Schlichting. - Moscow: Nauka Publishing House, 1974. - 712 p.] The Navier-Stokes equations and the continuity equation in cylindrical coordinates have the form

The boundary conditions determined by the condition of adhesion to a rotating plane will be

where p is the pressure;

ρ is the fluid density;

ν is the kinematic viscosity coefficient;

r, t, z - cylindrical coordinates;

V _t , V _r , V _z - velocity components in the tangential, radial and axial directions.

When superimposed on the rotation of the pulsation and radial-axial vibrations, according to the claimed method, creates a circulation of counter flooded flows of the working medium. In this case, factors such as the frequency and amplitude of oscillations that affect the components of the velocity of the liquid medium will already dominate.

We investigate the kinematic characteristics of the rotating disks 1 with a diameter D _d (Fig. 5) placed on the rotor 2, by means of which swirling countercurrent internal flooded jets of liquid are created, which, in addition to rotation with a frequency ω _{bp, are} informed of the velocity pulsations ± ε and radial-axial vibrations with a frequency ω and amplitude a.

Determine the maximum amplitude values of the components of the speed of the points on the periphery of the rotor disk

where a ₂ = R ₁ a / l;

and ₁ = ll ₁ / la.

The maximum fluid velocity will be in the peripheral zone of the lower disk (point A) (Fig. 5). At this point in time, the speed at point C is zero, since it is the instantaneous center of rolling.

Given the components of the velocities in the circumferential, radial and axial directions, the equations of motion of the liquid medium take the form

Moreover, the boundary conditions will be as follows

It is important to note that the new method of mixing allows us to simultaneously provide a number of physical effects: fluidization of the working fluid (turbulence), active mixing of the fluid (vibro-jet effect), the effect of vibrational rotation support.

In the turbulent mode, the liquid particles along with the main movement carry out transverse movements that create fluid mixing. Particle trajectories have a complex trajectory and intersect with each other. The transition of the laminar to turbulent regime occurs under certain conditions, characterized by the Reynolds number (criterion). When considering the flow of a liquid medium near the rotor disks, which rotates without oscillations, the Reynolds number will depend only on the tangential speed of the disks, while starting from a certain Reynolds number the flow ceases to be laminar [Schlichting G. Theory of the boundary layer / G. Schlichting. - Moscow: Publishing House "Science", 1974. - 712]. At Reynolds numbers

where ν is the kinematic viscosity of the liquid;

V is the peripheral speed of the disks; it is always turbulent.

If we consider the flow of a liquid medium near disks, which in addition to rotation also receives oscillations about an axis perpendicular to the plane of the disk, then the Reynolds number Re will be greater than the critical Re * (for similar methods Re *> 1000 [Ushakov V.G. Devices for mixing liquid media / VG Ushakov, EA Vasiltsov. - Kursk: Publishing house of KSTU, 2003. - 280 p.]). The nature of the change in fluid flows at each moment of time depends on different components of the velocity value, which affect the Reynolds number, the tangential component of the velocity V _{t having the} greatest value

where l _z is the distance between the disks;

D _p - the diameter of the tank.

The multiplicity of directions of the flooded jets allows you to provide the effect of fluidization of the fluid (Fig. 6), that is, the high-frequency vibrations of the working fluid created significantly increase its dynamic viscosity, thereby increasing the internal resistance of moving molecules (mixed components).

The radial-axial vibrations of the conical perforated discs mounted on the rotor of the vibratory mixer also create a vibro-jet effect (Fig. 7). That is, not only the speed of the stream of jets, but also the frequency of interaction of numerous flooded jets of liquid at the exit from the tapered conical holes increases. And this deepens the turbulization of the fluid. The intensity of the vibro-jet effect depends on the values of the axial velocity

The vibro-jet effect consists in different hydroresistance of conical holes when changing the direction of fluid movement through the latter. With an increase in the difference in the area of the openings at the inlet and outlet, the ratio of the resistances of the diffuser and confuser increases, i.e., a larger amount of liquid flows through the confuser (due to a sharper decrease in the amount of fluid flowing through the diffuser), thereby increasing the intensity of the vibro-jet effect at a constant speed of oscillation of the disk.

A rotor with disks, rotating with a frequency of ω _BP , will fluctuate due to its kinematic imbalance with a frequency ω greater than (10-100 times) the frequency of rotation of ω _BP . In this case, the fluid carried away by the oscillating rotor with the disks will also vibrate, which helps to maintain the rotation of the rotor disks, so the effect of vibrational support of the rotor rotation of the machine arises, the so-called Hula-Hoop effect (Fig. 8), which, in turn, allows to spend less power per rotation of the rotor in steady state. And this allows you to increase the energy efficiency of the process. In this case, the moment of forces of resistance to rotation of the rotor disks should not exceed a certain limiting value of the vibration moment W

At the same time, it is possible to realize all three of these effects if flooded jets are set to rotate with velocity pulsations and radial-axial vibrations, and this allows maximum turbulization of the liquid medium to be achieved, and therefore, to intensify the mixing process.

The conducted experimental studies made it possible to see even visually the presence of these physical effects (Fig. 9, Fig. 10). The formation of ring waves as a result of the interaction of internal flooded jets on the surface of a liquid medium is shown in FIG. 11, where the number of ring waves strictly corresponds to the number of diametrical rows of holes.

To assess the quality of the mixing process of the liquid - liquid systems, at the next stage of the experiments, mutually insoluble liquids - water and oil were used, and the optimal ratios between mixing time, axial force, and concentrations of water-oil mixture components were selected. The results are presented in FIG. 12, FIG. 13, FIG. fourteen.

For example, consider the following problem.

Determine the fluid velocity in the device with an inertial vibration actuator (Fig. 5), when the axial pressure of the rotor against the counterbody changes from 25 to 150 Η and the rotational speed of the rotor with discs changes from 4 to 15 rad / s (in the radial, axial and tangential directions ), under the following conditions:

- coefficient of kinematic viscosity ν = 15 · 10 ^-6 ;

- the density of the liquid medium ρ = 1000 kg / m ³ ;

- the radius of the rotor disk R ₁ = 0.07 m;

- radius of the rotor plate (radius of the circle described by the oscillation drive) R = 0.02 m;

- the diameter of the rotatable body in the area of its conjugation with the counterbody D = 0.04 m;

- the diameter of the disk D _d = 0,140 m

For a mathematical description of the flow of a working fluid, we use the Navier-Stokes equations and the continuity equation in a cylindrical coordinate system:

We rewrite the Navier-Stokes equation in dimensionless form, where all speeds take the form:

As a result, the Navier-Stokes equations and the continuity equation take the form:

and the oscillation frequency when using a device with a rotary inertial vibration actuator:

where R ₁ is the radius of the rotor disk;

R is the radius of the rotor plate (the radius of the circle described by the oscillation drive);

D _d - the diameter of the disk;

l - departure of the rotatable body;

l ₁ - the distance between the rotor plate and the disk,

m is the reduced mass of the rotated body;

j is the stiffness of the rotor;

D is the diameter of the rotated body in the area of its interface with the counterbody;

P _oc - axial pressing force to the rotor counterbody;

ω _BP - the rotational speed of the rotor with disks.

For example, when ω _bp = 4 rad / s, P _OS = 25 N:

We will integrate the resulting system of equations under the boundary conditions:

For numerical integration of a system of equations with the indicated boundary conditions, we use the Flow Vision program, which uses a method based on conservative schemes for calculating non-stationary partial differential equations that, in comparison with non-conservative schemes, give solutions that exactly satisfy conservation laws (in particular , continuity equation). To solve problems in the Flow Vision package, you should run a device model with the specified cost-effective parameters using an external program - a geometric preprocessor.

As such a preprocessor, we use, for example, the Solid Works package, which belongs to the CADob family (Computer-Aided Design), which are widely used in modern scientific and engineering practice.

The calculation results are presented in the table.

A tangible economic effect is expected from the introduction of the method of mixing liquids, since in modern methods of mixing and mixers there are a number of disadvantages that do not allow efficient mixing. Therefore, when replacing known designs of mixers with a mixer, which will be based on the proposed method of mixing, by increasing efficiency, productivity, their cost will significantly decrease.

Industrial applicability, therefore, of the proposed method can be implemented in the food industry, in the preparation of emulsions; in metal processing in the preparation of coolant, in mining in the preparation of drilling fluids and other industries where fluid mixing is required.

Claims (1)

A method of mixing liquid components, in which the mixtures are forced, with a frequency ω, by means of a rotor with perforated disks to set oscillating movements, forming unidirectional oncoming internal flooded jets, characterized in that the mixtures simultaneously specify rotation with velocity pulsations and radial-axial vibrations, at the same time , form swirling oncoming flooded jets and increase the length of their mixing path during volumetric circulation of these jets, and the parameters of these fluid motions are controlled by depending on

where r, t, z are cylindrical coordinates;
ν is the kinematic viscosity coefficient;
p is the pressure;
ρ is the density of the liquid medium;

- the amplitude of radial vibrations (in the area of the disk);

- amplitude of axial vibrations (in the zone of the disk);
ω is the oscillation frequency of the rotor with disks;
R ₁ is the radius of the rotor disk;
R is the radius of the circle described by the oscillation drive;
D _d - the diameter of the disk;
l - departure of the rotatable body;
l ₁ - the distance between the disk and the drive of its vibrations;
D is the diameter of the circle described by the oscillation drive;
ω _BP - the rotational speed of the rotor with the disks, while the amplitude of the oscillations of the rotor with the disks is

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