Hydrodynamic cavitation what. Hydrodynamic cavitation. The beneficial application of cavitation

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The review article analyzes the known methods of modeling the initial and developed stages of natural hydrodynamic cavitation. The distinctive features of this type of cavitation are briefly listed. When analyzing modern approaches to the description of its initial stage, two approaches were identified - stochastic (in the case of cavitation cavities in accordance with homogeneous and heterogeneous nucleation mechanisms) and deterministic (in the study of fluid motion near a dispersed spherical particle of variable radius). However, the differential distributions of cavitation nuclei over their radii used in known models are postulated based on experimental data. Moreover, within the framework of combining these approaches, modeling of the carrier phase of a heterogeneous medium in Euler variables and the dispersed one in Lagrange variables is actively developing. In the study of the developed stage, a deterministic approach using the theory of jets is used.

hydrodynamic cavitation

initial and advanced stages

stochastic and deterministic approaches

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When designing hydraulic regulating bodies for a pipeline system in which the shutter acts by the energy of the working medium in order to relieve increased or maintain a predetermined pressure level, to prevent back leaks, the problem of combating the undesirable effects of cavitation in fluid flows remains an urgent problem. In particular, these include damage to the internal surfaces of the flow channels of these devices in the form of erosive craters, as well as the resulting noise and vibration in the elements of pipe fittings. These factors affect the strength characteristics of this reinforcing equipment and impede the implementation of normal conditions for its operation in the framework of regulatory standards, including sanitary. The calculation of the flow part of the regulatory organs is associated with the assessment of a set of critical cavitation parameters, which, in particular, are introduced in accordance with the cavitation number κ \u003d 2Eu according to the Euler criterion and are determined by hydrodynamic and vibroacoustic methods. The manifestation of the primary cavitation effects in the bubble form is caused by a sharp drop in the liquid pressure to values \u200b\u200blower than the pressure of its saturated vapor (for example, at t \u003d 20.8 ° С for water - pH \u003d 2.5 · 10 3 Pa), due to the flow of the working medium through the flow part of the regulatory body when throttling or changing the direction of fluid flow. Thus, the description of the mechanism of behavior of cavitation bubbles in the processes of their evolution is of particular interest in the design of hydraulic control devices.

The purpose of the work is to analyze modern methods of modeling the main stages of development of the effect of hydrodynamic cavitation.

Short concept of hydrodynamic cavitation

Natural hydrodynamic cavitation is the effect of breaking the fluid flow, which, unlike acoustic cavitation (under the influence of sound waves), is observed when the pressure decreases to critical values \u200b\u200bin the local region of high-speed fluid flows. The physical nature of the phenomenon under consideration is also associated with transient thermodynamic processes (from metastable to stable state of the system) due to the fact that, simultaneously with a sharp decrease in the liquid pressure, it overheats. Modeling of fluid flows under conditions of natural hydrodynamic cavitation arising from a sharp drop in pressure during the flow of bodies of various shapes, for example, in pipeline systems when their integrity is impaired, in nozzles, in flowing parts of regulatory bodies (including when the valve is closed or closed opening with the extension of the stream), etc., is associated with solving many problems. These include a description of the mechanisms: the formation of the cavitation cavity, its expansion, contraction, collapse, etc., which correspond to the initial and developed stages of cavitation.

Modern approaches to modeling the initial stage of hydrodynamic cavitation

A. Stochastic approach. Separating the process of formation of these cavities in accordance with the homogeneous and heterogeneous nucleation mechanisms, a stochastic approach to their description should be distinguished: models of homogeneous nucleation; modifications with the introduction of a heterogeneity factor; models of heterogeneous nucleation, for example, on particles of impurities of a liquid medium, on a wall, in its cracks (depressions). Classical works by Ya.I. Frenkel, who continued the ideas of V. Volmer and A. Weber, supplemented by the research of J.N. Lienhard and A. Karimi with a proposal in theory to compare the work spent on the formation of a critical nucleon - W * with the minimum value of its potential energy (without specifying the kinetic energy of the molecules). As already noted, a critical nucleon is a vapor nucleus in a liquid medium with a metastable state. The nucleation frequency J (the number of nuclei in a unit volume per unit time) is determined by the formula

where is the Gibbs number; J * is a constant that depends on the values \u200b\u200bof the coefficients — the surface tension of the medium and the diffusion of gas in it, the number of liquid molecules, their volume; kB is the Boltzmann constant; Tl is the temperature of the liquid. In particular, expression (1) is used in the model of V.K. Kedrinsky to calculate the total volume of the diffusion layers Xd and the density of cavitation bubbles Nd (radius R and radius of the diffusion layer rd) per unit volume of the liquid medium (volcanic magma) using kinetic equations

Here, τ is the nucleation time of cavitation nuclei (induction period);   - the volume of the diffusion layer.

Modified models are used to describe the flow of a liquid medium with abrasive particles of small sizes. In this case, homogeneous nucleation may not be observed due to lower temperature changes (for example, for water less than ten times) in comparison with temperature drops for flows of purified liquid. The modification for J is represented in the form, where G is the heterogeneity factor, which characterizes the degree of decrease in the value of the work spent on the formation of a critical nucleon. Note that the most common are two forms of this factor in accordance with the works of Md. Alamgir, J.H. Lienhard and E. Ellas, P. L. Chambre

where T10, Tcr - initial and critical values \u200b\u200bof the temperature of the liquid, K; Vp is the pressure drop rate, Pa / s; σ is the excess free energy; ρV, ρl - phase densities (bubble and liquid); m is the molecular weight; b1, b2, b3, c1, c2 are constants. In addition, there are works that take into account the theory of homogeneous nucleation as part of the modification, as well as the subsequent expansion of cavitation cavities due to interfacial mass transfer. Note that the authors of the studies performed calculations for fluctuation nucleation under conditions of gas diffusion.

Of interest is a model of bulk heterogeneous nucleation, taking into account the size distribution of heterogeneous nuclei, which uses the approach from for the method of taking into account the corresponding experimental distribution (close to the lognormal) for impurity particles of cavitating fluid flows under acoustic effects. In the case according to the distributions of the centers of vaporization (in the form of normal, lognormal, and equiprobable laws) over the radii of these particles N (r), their number is estimated

As noted by the authors, S.G. Bankoff and Y.Y. Hsu, devoted respectively to heterogeneous nucleation on the wall and in its cracks, laid the foundation for further research in these areas. In this case, the criteria for the implementation of nucleation were identified: the difference in the free energy of volume nucleation exceeds the value of this value for the wall; the expansion of a hemispherical bubble in the cavity occurs if the temperature difference between the bubbles - indicated and equilibrium with the same radius, is greater than zero. In particular, T.S. Shin and O.C. Jones proposed an empirical relation for the frequency of heterogeneous nucleation on the wall in the form where, at c0 \u003d 10 4 and c \u003d 2.5 · 0 -8, the correlation of the bubble separation frequency nonlinearly depends on the temperature difference between the wall and the liquid, and the density of the formed bubbles is determined by their radii critical value of Rcr and at separation of Rd.

B. Deterministic approach. The deterministic approach, which is traditionally used to describe the behavior of a single cavitation bubble, is represented by the equation of motion (liquid near a dispersed spherical particle of variable radius) of the Rayleigh - Lamb (Rayleigh - Plesset) type, which has various modifications depending on the set of considered effects - inertial, thermal and diffusion. The general formulation of the boundary-value problem with a free boundary, which is presented in C-Di-Yu, for a distinguished surface that separates two regions: the inner - gas-vapor and the outer - liquid with dissolved gas, is usually transferred to the approximation of the spherical shape of the cavitation cavity. Moreover, this equation is a generalization of the system of equations in spherical coordinates: continuity, motion for the carrier phase, energy balance, thermal conductivity, diffusion and conditions at the interface. For example, neglecting diffusion and thermal factors, the classical Rayleigh-Lamb equation

when allows us to analyze the radial motion of the surface of a spherical cavity R (t) in an unbounded incompressible fluid with viscosity μl and density ρl taking into account the intensity of phase transitions ζlv on this surface and the phase pressure difference (pv - pl). Note that this case does not consider the case of a compressible fluid characteristic of acoustic cavitation. Of particular interest are the stability problems of a spherical bubble shape.

According to the behavior of the cavitation bubble on the wall, it can be represented as a complex movement (when decomposed into radial and translational) with a source (sink) in the center and replacement of the flow around the dipole when its moment is directed along the bubble movement. The method of mirror images allows us to describe the total potential of the flow of two symmetric dipoles and two fictitious sources, used to calculate the kinetic energy of the selected system. The system of Lagrange equations of the second kind in generalized coordinates (for the radius of the bubble and the distance from its center to the wall) makes it possible to estimate the rate of growth of the cavitation cavity near the wall.

B. Combined approach. The traditional method for modeling the flows of a liquid-vapor-gas system is heterogeneous with two phases (“carrier” - liquid and “dispersed” - a combination of vapor and gas) in the form of continua obeying the laws of a continuous medium generalized by R.I. Nigmatulin. At the same time, the system of characteristic equations is compiled in Euler’s spatio-temporal variables, when the desired functions, for example, the flow velocity, are specified at each point in space and its substantial time derivative makes sense. Another way to simulate the motion of these media is actively developing, when the carrier phase — the continuum (in Euler’s variables), and the dispersed one — forms a set of particles whose position is determined by the Lagrange variables — the coordinates in the selected reference frame at a given time. In this case, depending on the accuracy, it is proposed to search for the required functions for each phase when solving systems of equations for each phase separately, followed by clarifying the effect of interphase mass, pulsed, and energy transfers. In the framework of the problems of describing cavitation flows, in addition to the determinate equations of conservation of mass, momentum and energy, a stochastic approach can be used, for example, to analyze the nucleation frequency or estimate the change in the radius of the bubbles. In particular, in the work, the introduction of the concentration of vapor bubbles (including during heterogeneous nucleation on the wall and in the volume), supplemented by the equation of state of water in the form of the Theta condition, closes the Euler simulation stage. Moreover, the Rayleigh – Lamb equation at the Lagrangian stage is supplemented by the laws of conservation of mass and internal energy. A similar modeling method, but using the theory of homogeneous nucleation was used in the works.

The main methods for describing developed hydrodynamic cavitation

In theoretical terms, the description of the transitional stage from the initial to the developed stage of hydrodynamic cavitation remains problematic, while the problems of the stability of a developed cavity have a long history. Issues of studying the mechanism of partial closure of the cavity on the body (for example, during the movement of wings, screws, rotations of symmetrical objects, etc.) are usually considered from the standpoint of artificial cavitation (supercavitation), when the closure of the cavitation cavity on the body with the help of additional air blowing becomes complete, those. it completes behind the body at flow rates much lower than for the developed stages of natural cavitation. Experimental data on the shape of the cavity indicate the formation of a trickle in the region of its closure, which violates the integrity of the tail of the cavitation cavity and forms its vapor-gas trace. As a rule, in these cases the jet theory method is used, which extends the real flow of the medium to a conformal mapping using the desired transform function, which is specified in various ways. Known schemes for calculating plane flows: Kirchhoff, Zhukovsky - Roshko, Ryabushinsky, T. Wu, D.A. Efros, two representations of M. Tulin and their modifications. However, in this paper we restrict ourselves to setting out approaches with their possible application to the phenomenon of hydrodynamic cavitation in the flowing parts of pipeline regulatory bodies, i.e. in the case of the evolution of bubble cavitation.

According to the review, the degree of erosive influence of developed cavitation on the working surfaces of various hydrodynamic devices is determined by two factors, respectively, due to the asymmetric and symmetrical collapse of the cavitation cavity: the formation of a cumulative trickle near the wall (or when flowing around the body) with the subsequent possible hydraulic shock; the occurrence of spherical shock waves. For example, the work estimates the speed of the indicated trickle when a single cavity flows around the body, which allows you to calculate the cumulative flow pressure on the surface of the body. A numerical study of the direction of trickle development near an inclined wall was carried out in. The simulation of a high-speed shock jet in the form of a cylindrical column of liquid acting on an isotropic elastic half-space after the collapse of a cavitation bubble is presented in the paper. The author uses the Lagrange equations of the second kind to describe the complex motion of a single cavity with decomposition into radial and translational movements and applies the method of conformal mappings. The work of A. Thiruvengadam contains calculation formulas for the intensity of cavitation erosion, as well as the relative size of the nucleus, depending on the criteria of Weber, Mach and the number of cavitation. The description of the collapse of bubbles is associated with the tasks of acoustic cavitation, in particular, when using Kirwood-Bethe approximations for the motion of the surface of the cavity taking into account the compressibility of the fluid.

Conclusion

So, according to experimental data, the initial stage of development of hydrodynamic cavitation is divided into steam (in discontinuous cavities), gas (with the expansion of nucleons - gas nuclei) and vapor-gas. In addition, gas diffusion through the walls of vapor cavities and two types of nucleation are possible: homogeneous (fluctuation for the vapor phase in the liquid without impurities) and heterogeneous (for the gas system - vapor, suspended particles of impurities, walls and their cracks). In the developed stage, the compression and collapse of the cavities is observed the faster, the lower the gas content in their volume due to vapor condensation at the phase boundary with noise effects and water hammer from streamlined bodies. A significant gas content in the vapor-gas system leads to cavity pulsations due to possible adiabatic air compression with increasing temperature (up to values \u200b\u200bof the order of 10 3 ° С) and luminescence. An analysis of known literary sources has revealed the use of stochastic, deterministic approaches and their combinations at the stage of describing the initial stage of hydrodynamic cavitation. However, the differential distributions of cavitation nuclei over their radii used in known models are postulated based on experimental data. In the study of the developed stage, a deterministic approach using the theory of jets is used.

Bibliographic reference

  Kapranova A.B., Lebedev A.E., Meltzer A.M., Neklyudov S.V., Serov E.M. ON METHODS OF MODELING THE BASIC STAGES OF DEVELOPMENT OF HYDRODYNAMIC CAVITATION // Fundamental research. - 2016. - No. 3-2. - S. 268-273;
  URL: http://fundamental-research.ru/ru/article/view?id\u003d40043 (accessed September 16, 2019). We bring to your attention the journals published by the Academy of Natural Sciences publishing house

The term "Cavitation" comes from the Latin - Cavitas  (cavity, recess, cavity).
This term is used to denote a physical process that occurs under a number of conditions in liquids, and is accompanied by the formation and collapse of a large number of bubbles (voids, cavities).

Cavitation can be conditionally divided into two subtypes according to origin: hydrodynamic and acoustic.
In turn, hydrodynamic cavitation has two more subclasses - let's call them static and dynamic.

What is cavitation as a process of physicochemical property?
The effect of cavitation accelerated the deposition of salts from water, which led to jamming of the impeller of the NVV-25 pump.

P (atm.)T ° C
0.01 6.7
0.02 17.2
0.04 28.6
0.1 45.4
0.2 59.7
0.3 68.7
0.4 75.4
0.5 80.9
0.6 85.5
0.7 89.5
0.8 93
0.9 96.2
1 99.1
1.033 100

Water in nature is not a homogeneous and clean environment without impurities. All liquids are solutions in which a sufficiently large amount of impurities, mainly atmospheric gases. Almost two times more nitrogen than oxygen dissolves from atmospheric air in water.

So, approximately 665 ml of carbon dioxide are dissolved in 1 liter of water at a temperature of 20 ° C, and three times at 0 ° C
  more, 1995 ml. At a temperature of 0 ° C in one liter H 2 O  can be dissolved: He  - 10 ml H 2 s  - 4630 ml.

An increase in pressure entails an increase in the solubility of gases.

For example, at a pressure of 25 atm in 1 liter of water, 16.3 liters of carbon dioxide dissolve, and at 53 atm - 26.9. A decrease in pressure gives, accordingly, the opposite effect. If you leave the water tank overnight, gas bubbles form on the walls. This can be seen even more clearly and faster in a glass with soda. In the process of boiling water, we also see the process of formation of bubbles with gas and steam.

Cavitation (thermal) in a sense is the same boiling process caused not only by a rise in temperature
  (although this is also one of the factors in the formation of cavitation). In a combination of two factors, increased temperature and low pressure above the liquid, a cavitation process occurs in which the liquid passes into the gas-water mixture.

Pumping air out of a glass bottle with a vacuum pump - We obtain a cavitation “boiling” process at room temperature.

Video demonstration of the described effect.

This is especially critical and most often occurs in suction pump systems. The impeller or screw creates a vacuum in the suction line, which in the case of a lack of fluid at the inlet (narrowing of the passage, an excessive number of turns of the pipeline, etc.) creates conditions for cavitation boiling of the liquid.

Very often, customers come up with the question - why can not you suck up liquids with high temperature? The answer lies on the surface - with a decrease in pressure in the suction pipe, most of the water goes into the next state of aggregation, the so-called. water-gas mixture (in other words, cavitation boiling water), which can no longer be raised with a conventional water pump in principle.
A solution of a liquid with a gas is in equilibrium under ordinary conditions, i.e. the pressure in the liquid is greater than the pressure of the saturated vapor of the gas, and the system is stable. In those cases when this equilibrium is violated in the system, and the formation of cavitation bubbles occurs.
Consider the case of the formation of cavitation in a static system.

Most often, cavitation is formed in the zone located on the pressure line of the pump, in case of narrowing.
Those. the liquid pressure decreases after narrowing (according to Bernoulli's law), because losses and kinetic energy increase.
The saturated vapor pressure becomes greater than the internal pressure in the liquid with the formation of bubbles / caverns. After passing through a narrow part (it can be an ajar shutter, local narrowing, etc.), the flow velocity drops, the pressure increases and the gas and vapor bubbles collapse. Moreover, the energy released in this case is very, very large, as a result of which (especially if this occurs in the bubbles located on the walls), micro-hydroblows occur, which entail damage to the walls. In this case, if you do not take measures, the process will reach the complete destruction of the walls of the pumping part. Vibration and increased noise in the pump and pipes are the first signs of cavitation.

The main weak points in hydraulic systems are the places of narrowing, a sharp change in the fluid flow rate (valves, taps, valves) and the pump impellers. They become more vulnerable with an increase in surface roughness.

Accounting for pump cavitation at the system design stage.

To calculate a sufficient cavitation reserve of the system, you need to calculate
H  - the maximum possible suction height for these conditions, for a given pump and its performance.
,Where
Hf  - losses in the suction line (m.v.st.) in meters of water,
Hv  - pressure of saturated vapor of the liquid at the operating temperature (m),
Hs  - safety margin accepted by designers - 0.5 m.v.st.,
Pb  - pressure above the liquid - in an open system, this is atmospheric pressure, approximately equal to 10.2 m.v. ( Pb * 10.2)
Pump characteristic Npsh  (Net Positive Suction Head) means the suction height measured at the suction inlet to the pump, adjusted for the saturated vapor pressure of the specific fluid being pumped, at maximum pump performance.

Those. physical meaning of the formula H \u003d Pb * 10.2 - NPSH - Hf - Hv - Hs  consists in the fact that at the maximum operating parameters of the pump, the vacuum in its suction pipe does not exceed the pressure of saturated vapor of the liquid at the operating temperature, i.e. the system would have the support required for cavitation-free operation.

The other ways to reduce the likelihood of cavitation are quite obvious from here:
- change the suction diameter to a larger one - reduce losses ( Hf),
- move the pump closer to the fluid intake - reduce losses ( Hf),
- put a smoother pipe, reduce the number of turns, valves, valves - reduce losses ( Hf),
- reduce suction pressure by changing the pump height or using booster pump equipment - increase ( Pb),
- reduce the temperature of the liquid - reduce ( Hv),
- reduce pump performance, reduce speed - decrease ( Npsh).
All these measures are aimed at reducing the possibility of cavitation in the pump and lead to long-term and safe operation of the pumps.

The report presents some energy aspects that accompany work, widely touted as highly efficient.   heat sources. It was shown, in particular, that the occurrence of ultrahigh gradients of temperature and pressure is possible only in specially prepared “pure” homogeneous liquids. In the conditions of "technical" used in heating systems, the effects claimed by the project authors are fundamentally impossible.

Recently, in scientific and technical publications of a popular and informational orientation, including the Internet, they have been widely advertised.   hydrodynamic devicesintended, in particular, for use in local heating systems. The principle of operation of such devices at first glance seems quite simple.
  A characteristic feature of the numerous descriptions of such unique heaters is the almost complete absence of their theoretical justification, which does not allow, unfortunately, to quantify the objectivity of the claimed parameters.

Fig. 1. Schematic diagram of a small boiler house

In fig. 1, as an example, is a schematic diagram of a boiler room, the active element of which is   rotary, which is presented as a new generation of heat engines that convert mechanical, electrical and acoustic effects on a liquid into heat.

Rnrnrn rnrnrn rnrnrn

The increase in the temperature of the coolant occurs, according to the authors, due to the following effects: the conversion of mechanical energy due to internal friction arising from the movement of the coolant; the conversion of electrical energy into thermal energy due to the electro-hydraulic effect and heating of thermal elements; hydroacoustic energy into thermal energy due to cavitation and   swirl effects. In the diagram of Fig. 2 by the authors [ 1 ] the following notation is accepted: 1   - electric motor 2 - cavitation heat generator, 3   - pressure gauge 4   - boiler 5   - air cock, 6   - a heated coolant supply pipe, 7   - temperature sensor, 8   - automatic control unit, 9   - heat exchanger 10   - heating radiator, 11   - expansion tank, 12   - filter for cleaning the coolant, 13   - circulation pump.

Thus, the main element of the circuit is   cavitation heat generator 2 , which is in this case a rotary apparatus that are widely used in the chemical industry (for example, rotary devices of the GART class [ 2 ]). In addition to rotary devices, attempts are currently being actively advertised and conducted to scientifically substantiate the high energy performance of vortex devices constructed on the basis of   pipes Ranka [3 ].

Systems   cavitation heat generators, despite the most varied names (apparently the terminology of the second projects has not yet reached an agreement) consists of four main elements (Fig. 2): drive motor 1, pump 2, in fact   cavitation heat generator 3   through which the conversion of mechanical energy into   thermal energy  and thermal energy consumer 4.

Fig. 2. A typical structural diagram of a cavitation heat generator

Elements of a simplified block diagram 2   They are standard for almost any hydraulic system designed to transport liquid or gas.

The principle of operation of such energy transformers can be observed on the example of a public pump for watering beds and lawns in summer cottages. It is necessary to fill a regular three-liter can with water and make the pump take water from the can and discharge it there. Already through 5 - 10   minutes you can be sure that you are right   James Prescott Joule (1818 - 1889)  about the possibility of converting mechanical work into heat. The water in the jar will heat up. The effect is even brighter when the input and output of a home vacuum cleaner are “closed”. But this is a risky demonstration, the temperature rises so rapidly that you can not have time to separate the "input" and "output", which will lead to damage to the device.

The heater, the circuit of which is shown on, works approximately like a car engine cooling system, only the inverse problem is solved, not lowering the temperature, but increasing it. When starting the installation, the working fluid from the outlet   hydrodynamic cavitation  energy converter 3   by pump 2   served by a short way to the entrance   heat generator. After several circulations along the small (auxiliary) circuit, when the water reaches the set temperature, a second (working) circuit is connected. The temperature of the working fluid drops, but then, with successfully selected system parameters, it is restored to the desired value.

Numerous designs of activators advertised by manufacturers, in fact, are represented by devices that communicate kinetic energy to the working fluid. According to the authors of the projects, they succeed through the use of "special" design features   heat generators  and “non-traditional” physical effects to achieve high values \u200b\u200bof efficiency   h\u003e 0.9. In a number of intriguing cases   h, according to test results, exceeds one. Explaining such unusual characteristics of sufficiently studied hydrodynamic devices and processes, the researchers insist that they manage to use the unknown properties of cavitation phenomena (up to " cold"Thermonuclear fusion) or   torsion fieldsarising from the rotational motion of a fluid.

Typically, thermodynamic systems with   cavitation heat generators  less than one, and more often, two electric motors are used as the initial source of mechanical energy, which circulate the coolant through the system and create conditions for maintaining hydrodynamic cavitation. In other words, electric energy   E1  with corresponding losses   k1  converted to mechanical energy

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, (2)

where   k 2  - the conversion coefficient (in the terminology of the authors - the transformation) of the mechanical energy of the coolant flow into its internal energy, and the value varies, for the most part from 0,9   before 4 . If the value   k 2 @ 0.9  with certain theoretical simplifications, it can be considered as high, but to some extent real, then the values k 2 ≥ 1  require serious theoretical justification. The energy phenomenon is explained by the authors of the projects, in that their designs use a unique way of converting electrical energy into thermal energy through the use of “fluctuating vacuum in the conditions of severe cavitation” and “energy of water molecules”.

Without further discussing, for obvious reasons, the torsion and thermonuclear problems, as well as the energy of the physical vacuum, we consider some features of using the energy effects of hydrodynamic cavitation in the body and mass transfer processes. The processes of boiling, acoustic and hydrodynamic cavitation can be represented as the phenomenon of formation of a competitive phase in a continuous liquid in the form of cavities filled with steam, a working fluid and dissolved gases.

We note that the phenomenon of hydrodynamic and acoustic cavitation, despite more than a century of study, does not seem to be fully described. All researchers involved   cavitation  processes, agree that the phenomenon in some of its manifestations is not yet predictable. The parameters of engineering structures and devices, the operation of which is associated with the occurrence and course of cavitation (hydraulic turbines, ship propulsion, pumps, mixing devices, technological plants), along with the results of theoretical studies are supplemented by experimental data, the basis of which is modeling   cavitation  phenomena at special stands [ 4-7 ]. However, much is already known about cavitation. At least, to date, the basic laws associated with its occurrence and course have been established. Scientists and engineers have learned quite successfully to prevent destructive manifestations (for example, super-cavitating ship propellers) and use them in technological processes when something needs to be destroyed, for example, particles of insoluble liquids, or organize chemical reactions that do not proceed under ordinary conditions.

Researchers have paid attention to the energy effects accompanying the appearance of a competitive phase in a liquid under pressure conditions commensurate with the pressure of saturated vapor of the working fluid. IN   1917  Lord Rayleigh solved the problem of pressure developing in a liquid when a "empty" spherical cavity collapses [ 4 ]. For the case of spherical symmetry in an irrotational radial flow of a fluid surrounding a cavity, the equation of kinetic energy was obtained   K L

, (3)

where p L  - fluid density   u  - radial speed at an arbitrary distance   r\u003e R  from the center of the cavity v r  - radial velocity of the cavity wall. In accordance with the theorem, the change in the kinetic energy of a liquid should be equal to the work performed by the mass of liquid when the cavity is closed

(4)

where is the pressure in the liquid at a distance R max  - the radius of the cavity at the time of the beginning of its collapse,   R 0  - the final radius of the cavity. Equating ( 3 ) and ( 4 ), we can come to the equation of the velocity of the surface of the spherical cavity

. (5)

So, for example, for the case   R max \u003d 10 -3 m  and R 0 \u003d 10 -6 m  at   \u003d 105 Pa, p L \u003d 103 kg / m 3  the speed of the cavity wall is equal to v r @ 1, 4 × 10 4 m / s, which is an order of magnitude greater than the speed of sound in water. The kinetic energy of the liquid filling the cavitation cavity will be in accordance with the equation ( 3 ) value

, (6)

Assuming that only 10%   Since the kinetic energy of the liquid is converted into heat, the maximum local temperature change in the region of the collapse of the cavity will be approximately

where   s @ 4200 J / kg × K  - specific heat of water. It is natural to assume that processes at the molecular and atomic levels are possible at such high temperatures. It must be assumed that it was precisely such calculation results that led the designers of cavitation heat generators to the assumptions about the possibility of reactions of "cold" fusion.

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Table 1

It should be borne in mind that the calculations are based on the theory of an unlimited increase in the pressure and velocity of the boundaries of the cavity at the final stages of closure in an ideal fluid with ultimate bulk strength z, the theoretical values \u200b\u200bof which are given in table. 1 .

Under the influence of pressures and temperatures, the intermolecular distances in a fluid can change, and when a limit is reached that is completely defined for each fluid, continuity breaks. So for example, for water, the intermolecular distance is L 0 @ 3 × 10 -10 m , which allows us to determine the maximum tensile stress as

. (8)

The data of M. Kornfeld were obtained for the case of the appearance of a competitive vapor phase simultaneously in the entire volume of liquid, which is never observed in practice. If water had the indicated strength, then get   cavitation  in the conditions of the discussed devices it would be impossible. In practice, in conditions of specially prepared portions of liquids that do not contain inhomogeneities, vapor cores can occur due to thermal fluctuations. An increase in the volume of vapor nuclei is possible if the saturated vapor pressure of the liquid exceeds the external pressure, i.e.

, (9)

where p sp  - pressure of saturated vapor of the liquid, s L / sp - coefficient of surface tension at the liquid-vapor interface. The number of nuclei capable of losing stability per unit time in a unit volume of liquid is determined by the equation of Ya.B. Zeldovich [ 5 ]

, (10)

where n 0   - the number of nuclei formed,   F  is a constant factor k B@ 1,4 × 10 -23 J / C  - Boltzmann constant   T  - absolute temperature A (R 0 )   - core formation work

the first term describes the amount of energy spent on creating a free surface, the second term ( 11 ) is the work of forming a new cavity with a radius R 0, third - the work necessary to fill the cavity with steam.
  Thus, in order to create microinhomogeneities in a homogeneous fluid by external forces, a certain work must be done. In other words, a change in the state of the fluid, including the formation of   cavitation  nuclei, occurs due to the supply of energy from external sources. Formed   cavitation  the core can increase or decrease its volume depending on the ratio of external pressure and vapor pressure inside the core. The kernel growth condition can be obtained by combining the equations ( 11 ) and ( 10 ), i.e. from the equation ( 11 ) determine the value R 0  and substitute this value in the condition ( 9 )

, (12)

where   1 / t \u003d dn 0 / dt,   t  - waiting time for the gap in the continuity of a unit volume of liquid. Assuming that unit   cavitation  core in volume   1 cm 3  formed within one second and taking according to Kornfeld   A @ 10 3 1 s - 1 m 3  it turns out

In this case

.(12)

In accordance with ( 12 ) the tensile strength for water is equal to   z @ 1,6 × 10 8 Pa, almost two times less than the theoretical value of Kornfeld and three times less than the molecular equation ( 8 ).

As established experimentally [ 4 - 7 ],   cavitation  the strength of liquids is several orders of magnitude lower than theoretical values. So, for example, M.G. Sirotyuk [ 7 ] and G. Flynom [ 6 ] measurement data published   cavitation  durability of distilled purified and tap water. When measuring the threshold values \u200b\u200bof acoustic pressure at different frequencies at which the occurrence of a competitive phase was recorded, the minimum pressure values \u200b\u200bfor untreated tap water were obtained p  c r @ 5 × 10 4 Pa, and for distilled prepared water - p  c r @ 4 × 10 7 Pa.

Fig. 3. Experimental thresholds for cavitation in water

The main reason for this significant variation   cavitation  strength of water is its heterogeneity, i.e. presence in her   cavitation nuclei filled with gas and liquid vapors, in other words, the appearance of a competitive phase occurs on nuclei of critical radius already present in the liquid R   c r   when they enter the zone of reduced pressure.

If we assume that the process of expansion of the nucleus proceeds according to an adiabatic scheme, then the relationship of the initial P G (0)   and current P g  gas pressure in a volume-increasing core can be represented on the basis of the Poisson equation can be represented as follows

where g   is the adiabatic index. In this case, the kinematic parameters adjacent to the core that changes its volume can be expressed by the following differential equation [ 5 ]

. (14)

For the maximum value of the radial velocity component, instead of the equation ( 5 v r (max) @   534 m / s, what in 26   times smaller hypothetical temperature gradient in accordance with the equation ( 7 ) will be

,(16)

which is incomparably less than the "thermonuclear" temperatures, which are mentioned in publications devoted to   cavitation heat generators. It should also be borne in mind that in heating systems, ordinary tap water with a high gas content is used, in which relatively large   Cavitation  gas filled cores. If such nuclei fall into the zones of low pressure, the nuclei will increase their volume to a certain maximum value, and then their volume will periodically change at the natural frequency

. (18)

The energy stored by the cavitation cavity will be partially generated in the form of acoustic vibrations, with a coefficient of transformation into thermal energy not exceeding 1%   of the total energy of the cavity.

Keep in mind hydrodynamic systems   cavitation heat generators  are closed (Fig. 2), which suggests the presence of a circulation circuit. The fluid that has passed the zone of low pressure in the heat generator after a short time again gets there. This fluid circulation through the cavitation zone is characterized by hysteresis phenomena [ 8 ], when the number and size distribution of cavitation nuclei changes.   Cavitation  fluid strength decreases, gas-filled bubbles circulate in the system, with dimensions that do not allow them to reach the water surface in the expansion tank (Fig. 1).

Thus, on the basis of the analysis we can conclude that under the conditions of heat generators, hydrodynamic cavitation cannot be considered as a source of additional energy. An ensemble of expanding, collapsing and pulsating   cavitation the cavern is presented as a kind of energy energy transformer, the efficiency of which, in principle, like any transformer, cannot exceed unity.

Literature

    tstu.ru/structure/kafedra/doc/maxp/eito6.doc

    Friedman V.M. Ultrasonic chemical equipment. - M.: Mechanical Engineering, 1967. - 211 p.

    Potapov Yu.S., Fominsky L.P., Vortex energy and from the standpoint of the theory of motion. - Chisinau - Cherkasy: OKO-Plus. , 2000. - 387 p.

    Knepp R., Daily J., Hammit F. Cavitation. - M .: Mir, 1974. - 678 p.

    Pernik A.D. Cavitation problems. - L .: Shipbuilding, 1966. - 435 p.

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    Flynn G. Physics of acoustic cavitation in liquids. In the book. Physical Acoustics, // Ed. W. Mason, T 1, - M .: Mir, 1967, S. 7 - 128.

    Sirotyuk M.G. Experimental studies of ultrasonic cavitation. In the book. Powerful ultrasonic fields, // Ed. L.D. Rosenberg, 1968.S. 168 - 220.

    Vasiltsov E.A., Isakov A.Ya. Hysteresis properties of cavitation // Applied Acoustics. Vol. 6. -Taganrog: TRTI, 1974. -P.169-175.

 

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