Hydrodynamic cavitation what. hydrodynamic cavitation. Useful application of cavitation

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The review article analyzes the known methods for modeling the initial and advanced stages of natural hydrodynamic cavitation. The distinctive features of this type of cavitation are briefly listed. When analyzing modern approaches to describing its initial stage, the use of two approaches was revealed - stochastic (in the case of the formation of cavitation cavities in accordance with homogeneous and heterogeneous nucleation mechanisms) and deterministic (in the study of fluid motion around a dispersed spherical particle of variable radius). However, the differential distributions of cavitation nuclei over their radii, used in known models, are postulated on the basis of experimental data. At the same time, within the framework of combining these approaches, the modeling of the carrier phase of a heterogeneous medium in Euler variables, and the dispersed one in Lagrange variables, is being actively developed. When studying the developed stage, a deterministic approach is used using the jet theory method.

hydrodynamic cavitation

early and advanced stages

stochastic and deterministic approaches

1. Aganin A.A. Calculation of the force impact of a cavitation bubble on an elastic body / A.A. Aganin, V.G. Malakhov, T.F. Khalitova, N.A. Khismatullina // Bulletin of the TSGPU. - 2010. - T. 22. - No. 4. - P. 6–12.

2. Aiveni R.D. Numerical analysis of the phenomenon of collapse of a cavitation bubble in a viscous liquid / R.D. Ivani, F.G. Hammit // Tr. ASME. Ser. D. Theoretical methods of engineering calculations. - 1965. - No. 4. - C. 140.

3. Arzumanov E.S. Cavitation in local hydraulic resistances. – M.: Energy, 1978. – 304 p.

4. Afanasiev K.E. Numerical modeling of the dynamics of spatial steam-gas bubbles / K.E. Afanasiev, I.V. Grigorieva // Computational technologies. - T. 11, spec. release. – P. 4–25.

5. Blagov E.E. Calculation of integral hydrodynamic indicators of pipeline narrowing devices // Armaturostroyeniye. - 2006. - No. 6 (45). – P. 44–49.

6. GOST R 55508-2013. Pipe fittings. Method of experimental determination of hydraulic and cavitation characteristics. – M.: Standartinform, 2014. – 38 p.

7. Kedrinsky V.K. On gas-dynamic signs of explosive volcanic eruptions. 1. Hydrodynamic analogues of the pre-explosion state of volcanoes, dynamics of the state of three-phase magma in decompression waves, Priklad. mechanics and tech. physics. - 2008. - T. 49. - No. 6. - P. 3-12.

8. Knepp R. Cavitation / R. Knepp, J. Daley, F. Hammit. – M.: Mir, 1974. – 668 p.

9. Ksendzovsky P.D. Calculation of erosion impact on a streamlined airfoil under bubble cavitation // Issledovanie i raschet gidromashiny. Tr. VNIIGidromash. – M.: Energy, 1978. – S. 27–42.

10. Kulagin V.A. Modeling of two-phase supercavitational flows / V.A. Kulagin, A.P. Vilchenko, T.A. Kulagina; under. ed. IN AND. Bykov. - Krasnoyarsk: CPI KSTU, 2001. - 187 p.

11. Kulagin V.A. Supercavitation in power engineering and hydraulic engineering. - Krasnoyarsk: CPI KSTU, 2000. - 107 p.

12. Kumzerova E.Yu. Numerical modeling of the formation and growth of vapor bubbles under conditions of a drop in liquid pressure: Ph.D. dis. ... cand. Phys.-Math. Sciences. 01.02.05. - St. Petersburg, 2004. - 15 p.

13. Lavrinenko O.V. Modeling of mechano-physicochemical effects in the process of collapse of cavitation cavities / O.V. Lavrinenko, E.I. Savina, G.V. Leonov // Polzunov collection. - 2007. - No. 3. - P. 59–63.

14. Levkovsky Yu.L. The structure of cavitation flows. - L .: Shipbuilding, 1978. - 224 p.

15. Markina N.L. Study of cavitation processes in a channel with a variable section / N.L. Markina, D.L. Reviznikov, S.G. Cherkasov // Izvestiya RAN. Energy. - 2012. - No. 1. - P. 109–118.

16. Nigmatulin R.I. Fundamentals of mechanics of heterogeneous media. – M.: Nauka, 1978. – 336 p.

17. Oksler G. Cavitation in fittings? Let's figure it out! // Armature building. - 2012. - No. 2 (77). – S. 74–77.

18. Pirsol I. Cavitation. – M.: Mir, 1975. – 95 p.

19. Rozhdestvensky V.V. cavitation. - L .: Shipbuilding, 1977. - S. 148.

20. Si-Ding-Yu. Some analytical aspects of bubble dynamics // Proceedings of the American Society of Mechanical Engineers. Series D. - 1965. - T. 87. - No. 4. - S. 157-174 (translated from English).

21. Flynn G. Physics of acoustic cavitation in liquids // Physical Acoustics / ed. W. Mason. - M.: Mir, 1967. - T. 1. - S. 7-138.

22. Frenkel Ya.I. Kinetic theory of liquids. - L.: Nauka, 1959. - 586 p.

23. Alamgir Md. Correlation of pressure undershoot during hot-water depressurization / Md. Alamgir, J.H. Lienhard // Journal of Heat Transfer. - 1981. - Vol. 103. - No. 1. - P. 52–55.

24. Bankoff S.G. Entrapment pf gas in the spreading of a liquid over a rough surface // AlChE Journal. - 1951. - Vol. 4. – P. 24–26.

25. Brennen C.E. Cavitation and bubble dynamics. - New York, Oxford University Press, 1995. - 294 p.

26. Ellas E. Bubble transport in flashing flow / E. Ellas, P.L. Chambre // Int J. Multiphase Flow. - 2000. - No. 26. - P. 191–206.

27. Hsu Y.Y. On the size range of active nucleation cavities on a heating surface // Journal of Heat Transfer. - 1962. - Vol. 94. – P. 207–212.

28. Kedrinskii V.K. The lordansky-Kogarko-van Wijngaarden model: shock and rarefaction wave interactions in bubbly media // Applied Scientific Research. - 1998. - Vol. 58. – P. 115–130.

29. Kwak H.-Y. Homogeneous nucleation and macroscopic growth of gas bubble in organic solutions / H.-Y. Kwak, Y.W. Kim // Int. J. Heat and Mass Transfer. - 1998. - Vol. 41. - No. 4–5. - P. 757-767.

30. Lienhard J.N. Homogeneous nucleation and the spinodal line / J.N. Lienhard, A. Karimi // Journal of Heat Transfer. - 1981. - Vol. 103. - No. 1. - P. 61–64. Lienhard J.N., Karimi A. Homogeneous nucleation and the spinodal line // Journal of Heat Transfer. - 1981. - Vol. 103. - No. 1. - P. 61–64.

31. Neppiras E.A. Acoustic cavitation // Phys. Reps. - 1980. - Vol. 61, No. 3. - P. 159-251.

32. Pleset M.S. Collapse of an Initially Spherical Vapor in the Neighborhood of a Solid Boundary / M.S. Pleset, R.B. Chapman // Journal of Fluid Mechanics. - 1971. - Vol. 47. - No. 2. - P. 125-141.

33. Shin T.S. Nucleation and flashing in nozzles-1. A distributed nucleation model / T.S. Shin, O.C. Jones // Int. J. Multiphase Flow. - 1993. - Vol. 19. - No. 6. - P. 943-964.

34. Sokolichin A. Dynamic numerical simulation of gas-liquid two-phase flows: Euler/Eler versus Euler/Lagrange / A. Sokolichin, G. Eigenberger, A. Lapin, A. Lubbert // Chemical Eng. Science. - 1997. - Vol. 52. – P. 611–626.

35. Thiruvengadam A. Scaling Law for Cavitation Erosionc // Unsteady water flows with high speeds: Proceedings of LITAM. - M.: Nauka, 1973. - S. 405-427.

36. Volmer V. Keimbildung in uebersaetigen Daempfen / Vol. Volmer, A. Weber // Z. Phys. Chem. - 1926. - No. 119. - P. 277-301.

When designing hydraulic regulators for a pipeline system, in which the action on the valve is carried out due to the energy of the working medium in order to relieve increased or maintain a given pressure level, prevent back leakage, the problem of combating the undesirable consequences of the cavitation effect in fluid flows remains relevant. In particular, these include damage to the internal surfaces of the flow channels of these devices in the form of erosion craters, as well as the resulting noise and vibration in the elements of pipeline valves. The listed factors affect the strength characteristics of this reinforcing equipment and prevent the implementation of normal conditions for its operation within the framework of regulatory standards, including sanitary ones. The calculation of the flow part of the regulating 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 = 2Eu according to the Euler criterion and are determined by hydrodynamic and vibroacoustic methods. The manifestation of primary cavitation effects in a bubble form is caused by a sharp drop in liquid pressure to values ​​lower than its saturated vapor pressure (for example, at t = 20.8 ° C for water - pH = 2.5 10 3 Pa), due to the flow of the working medium through the flow part of the regulating body when throttling or changing the direction of the 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 modeling of the main stages of development of the effect of hydrodynamic cavitation.

Brief concept of hydrodynamic cavitation

Natural hydrodynamic cavitation is the effect of fluid flow disruption, which, in contrast to acoustic cavitation (under the influence of sound waves), is observed when the pressure drops to critical values ​​in the local region of high-speed fluid medium flows. The physical nature of the phenomenon under consideration is also associated with transient thermodynamic processes (from the metastable to the stable state of the system) due to the fact that, simultaneously with a sharp decrease in the pressure of the liquid, its overheating occurs. Simulation of flows of liquid media under conditions of natural hydrodynamic cavitation arising from a sharp drop in pressure in the process of flow around bodies various shapes, for example, in pipeline systems in case of violation of their tightness, in nozzles, in the flow parts of regulatory bodies (including during valve operation - it closes or opens with flow expansion), etc., is associated with solving many problems. These include a description of the mechanisms: the formation of a cavitation cavity, its expansion, compression, collapse, etc., which correspond to the initial and advanced 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 homogeneous and heterogeneous mechanisms of nucleation, one should single out a stochastic approach to their description: models of homogeneous nucleation; modifications with the introduction of a heterogeneity factor; models of heterogeneous nucleation, for example, on particles of impurities in a liquid medium, on a wall, in its cracks (depressions). Classical works of 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 to theoretically 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 molecules). As already noted, the 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 ​​of the coefficients - the surface tension of the medium and the diffusion of gas in it, the number of liquid molecules, their volume; kB - Boltzmann's constant; Tl is the liquid temperature. In particular, expression (1) is used in the model of V.K. Kedrinsky to calculate the total volume of diffusion layers Xd and the density of cavitation bubbles Nd (radius R and diffusion layer radius rd) per unit volume of a liquid medium (volcanic magma) using kinetic equations

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

The modified models are used to describe the flows of a liquid medium with small abrasive particles. In this case, homogeneous nucleation may not be observed due to lower values ​​of temperature change (for example, for water, ten times less) in comparison with temperature drops for purified liquid flows. The modification for J is represented as , where G is the heterogeneity factor, which characterizes the degree of decrease in the value of the work spent on the formation of the 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 are the initial and critical values ​​of the liquid temperature, K; Vp - rate of pressure drop, Pa/s; σ - excess free energy; ρV, ρl are 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 gas diffusion conditions.

Of interest is the model of bulk heterogeneous nucleation, which takes into account the size distribution of heterogeneous nuclei, in which the approach from is used to take into account the corresponding experimental distribution (close to lognormal) for impurity particles of cavitating liquid 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) according to the radii of these particles N(r), their number is estimated

As noted by the authors, the works of 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 directions. At the same time, the criteria for the implementation of nucleation were revealed: the difference in the free energy of bulk nucleation exceeds the value of this value for the near-wall ; expansion of a hemispherical bubble in the cavity occurs if the difference between the temperatures of 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 critical value of Rcr and at separation Rd.

B. Deterministic approach. The deterministic approach, traditionally used to describe the behavior of a single cavitation bubble, is represented by the Rayleigh-Lamb (Rayleigh-Plesset) equation of motion (of a fluid around a dispersed spherical particle of variable radius), which has various modifications depending on the set of considered effects - inertial, thermal and diffusion. The general formulation of a boundary value problem with a free boundary, which is presented in the work of Xi-Di-Yu, for a selected surface that separates two regions: the inner one - vapor-gas and the outer one - liquid with dissolved gas, is usually transferred to the approximation of the spherical shape of the cavitation cavity. In this case, this equation is a generalization of the system of equations in spherical coordinates: continuity, movement 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

at allows one to analyze the radial motion of the surface of a spherical cavity R(t) in a boundless incompressible fluid with viscosity μl and density ρl, taking into account the intensity of phase transitions ζlv on the specified surface and the phase pressure difference (pv - pl). Note that this presentation does not consider the case of a compressible fluid, which is characteristic of acoustic cavitation. Problems of stability of a spherical bubble shape are of particular interest.

The behavior of the cavitation bubble on the wall according to can be represented as a complex motion (when decomposed into radial and translational) with the source (sink) in the center and the replacement of the flow around by a dipole with the direction of its momentum along the movement of the bubble. The mirror image method allows one to describe the total flow potential of two symmetric dipoles and two fictitious sources, which is used to calculate the kinetic energy of a 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. A traditional method is known for modeling the flows of a liquid - vapor - gas system, as heterogeneous with two phases ("carrier" - liquid and "dispersed" - a combination of steam and gas) in the form of continuums that obey the laws of a continuous medium, generalized by R.I. Nigmatulin. In this case, the compilation of a system of characteristic equations in the space-time Euler variables is realized, when the desired functions, for example, the flow velocity, are specified at each point in space and its substantial time derivative makes sense. Another method of modeling the motion of these media is being actively developed, when the carrier phase is a continuum (in Euler variables), and the dispersed phase forms a set of particles whose position is given by Lagrange variables - coordinates in the selected reference frame at a given time. At the same time, depending on the accuracy, it is proposed to find the desired functions for each phase when solving systems of equations for each phase separately, followed by refinement of the influence of interphase mass, impulse and energy transfers. In the framework of the problems of describing cavitation flows, in addition to the deterministic equations of conservation of mass, momentum, and energy, one can use the stochastic approach, for example, to analyze the nucleation frequency or estimate the change in the radius of bubbles. In particular, in this work, the introduction of the concentration of vapor bubbles (including in the case of heterogeneous nucleation on the wall and in the volume), supplemented by the equation of state of water in the form of the Theta condition, leads to the closure of the Euler stage of modeling. In this case, 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. The issues of studying the mechanism of partial closure of a cavity on the body (for example, during the movement of wings, propellers, 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 injection becomes complete, those. ends 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 part of the cavitation cavity and forms its vapor-gas wake. 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 required transforming function, which is given by different ways. Known schemes for calculating flat 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 the presentation of approaches with their possible application to the phenomenon of hydrodynamic cavitation in the flow parts of pipeline control elements, 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 jet near the wall (or when flowing around a body) with subsequent possible water hammer; the emergence of spherical shock waves. For example, in this paper, the velocity of the indicated jet was estimated when a single cavity flows around a body, which allows calculating the pressure of the cumulative flow on the body surface. A numerical study of the direction of development of a trickle near an inclined wall was carried out in . Modeling 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 author applies the Lagrange equations of the second kind to describe the complex motion of a single cavity with decomposition into radial and translational motions and uses 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 core, depending on the Weber, Mach criteria and cavitation number. The description of the collapse of bubbles is related to the problems of acoustic cavitation, in particular, when using the Kirwood-Bethe approximations for the movement of the cavity surface, taking into account the compressibility of the liquid.

Conclusion

So, the initial stage of the development of hydrodynamic cavitation, according to experimental data, is divided into steam (in discontinuous cavities), gas (during the expansion of nucleons - gas nuclei) and steam-gas. In addition, gas diffusion through the walls of vapor cavities and two types of nucleation are possible: homogeneous (fluctuation for a vapor phase in a liquid without impurities) and heterogeneous (for a gas-vapor system of suspended particles of impurities, walls and their cracks). In the developed stage, the compression and collapse of the cavities is observed the faster the less content gas 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 steam-gas system leads to cavern pulsations due to possible adiabatic air compression with an increase in temperature (up to values ​​of the order of 10 3 °C) and glow. An analysis of known literary sources 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 on the basis of experimental data. When studying the developed stage, a deterministic approach is used using the jet theory method.

Bibliographic link

Kapranova A.B., Lebedev A.E., Meltzer A.M., Neklyudov S.V., Serov E.M. ON METHODS OF SIMULATION OF THE MAIN STAGES OF DEVELOPMENT OF HYDRODYNAMIC CAVITATION // Basic Research. - 2016. - No. 3-2. – S. 268-273;
URL: http://fundamental-research.ru/ru/article/view?id=40043 (Accessed 09/16/2019). We bring to your attention the journals published by the publishing house "Academy of Natural History"

The term "cavitation" comes from the Latin - Cavitas(depression, deepening, 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 roughly divided into two subtypes according to its 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 physical and chemical properties?
The impact of cavitation accelerated the precipitation of salts from the 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 pure medium without impurities. All liquids are solutions in which a sufficiently large amount of impurities, mainly atmospheric gases. From atmospheric air, almost twice as much nitrogen dissolves in water as oxygen.

So, in 1 liter of water at a temperature of 20 ° C, approximately 665 ml of carbon dioxide dissolves, and at 0 ° C - three times
more, 1995 ml. At a temperature of 0°C in one liter H2O 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, 16.3 liters of carbon dioxide dissolve in 1 liter of water, and at 53 atm - 26.9. Lowering the pressure gives, respectively, the opposite effect. If you leave a container of water overnight, gas bubbles form on the walls. Even more clearly and quickly it can be seen in a glass of soda. In the process of boiling water, we also see the formation of bubbles with gas and steam.

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

Pumping out air from a glass bottle with a vacuum pump - We get the process of cavitation "boiling" at room temperature.

Video demonstration of the described effect.

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

Very often, customers ask the question - why is it impossible to suck up liquids with high temperatures? The answer lies on the surface - when the pressure in the suction pipe decreases, most of the water passes into the next state of aggregation, the so-called. a 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 normal conditions, i.e. the pressure in the liquid is greater than the saturated vapor pressure of the gas, and the system is stable. In those cases when this equilibrium is disturbed in the system, and cavitation bubbles are formed.
Let us consider the case of Cavitation formation in a static system.

Most often, cavitation is formed in the area located on the pressure line of the pump, in case of its narrowing.
Those. the fluid pressure after the constriction drops (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 the narrow part (this may be an ajar valve, local constriction, 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 happens in bubbles located on the walls) micro-hydraulic shocks occur, resulting in damage to the walls. At the same time, if no measures are taken, 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 places of narrowing, a sharp change in the fluid flow rate (valves, taps, gate valves) and pump impellers. They become more vulnerable with increasing surface roughness.

Accounting for the cavitation reserve of the pump at the stage of system design.

To calculate the sufficient cavitation reserve of the system, it is necessary to calculate
H- the maximum suction height possible for given conditions, for a given pump and its performance.
,where
hf- losses in the suction line (m.w.st.) in meters of water column,
hv- saturated vapor pressure of the liquid at operating temperature (m),
hs- safety margin accepted by designers - 0.5 m.w.st.,
Pb- pressure above the liquid - in open system this is atmospheric pressure, approximately equal to 10.2 m.w.st. ( Pb*10.2)
Pump characteristic NPSH(Net Positive Suction Head) means the suction head measured at the suction inlet of the pump, corrected for the saturation vapor pressure of the specific liquid being pumped, at the maximum pumping capacity.

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

From here, other ways to reduce the likelihood of cavitation are quite obvious:
- change the suction diameter to a larger one - to reduce losses ( hf),
- move the pump closer to the liquid intake point - reduce losses ( hf),
- put a smoother pipe, reduce the number of turns, gate valves, valves - reduce losses ( hf),
- reduce the vacuum at the suction by changing the height of the pump installation or using booster pumping equipment - increase ( Pb),
- reduce the temperature of the liquid - reduce ( hv),
- reduce the pump performance, reduce the number of revolutions - lower ( 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 message presents some of the energy aspects that accompany the work, widely advertised as highly efficient thermal energy sources. It is shown, in particular, that the occurrence of ultrahigh temperature and pressure gradients is possible only in specially prepared "pure" homogeneous liquids. In the conditions of the "technical" used in heating systems, the effects declared by the authors of the projects are fundamentally impossible.

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

Rice. 1. Schematic diagram of a small boiler house

On fig. 1, as an example, a schematic diagram of a boiler house is presented, 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; transformation 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 vortex effects. In the diagram of Fig. 2, the authors [ 1 ] the following designations are accepted: 1 - electric motor, 2 - cavitation heat generator, 3 - manometer, 4 - boiler, 5 - air faucet, 6 - heated coolant supply pipeline, 7 - temperature sensor 8 - block automatic control, 9 - heat exchanger, 10 - heating radiator, 11 - expansion tank, 12 - a filter for cleaning the coolant, 13 - circulation pump.

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

Systems cavitation heat generators, despite the most diverse names (the authors of the projects, apparently, have not yet managed to agree on the terminology) consists of four main elements (Fig. 2): drive motor 1, pump 2, actually cavitation heat generator 3 through which mechanical energy is converted into thermal energy and consumer of thermal energy 4.

Rice. 2. Typical block diagram of a cavitation heat generator

Simplified block diagram 2 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 publicly available pump for watering beds and lawns in summer cottages. It is necessary to fill an ordinary three-liter jar with water and force the pump to take water from the jar and dump it there. Already through 5 - 10 minutes, you can be sure of the complete correctness James Prescott Joule (1818 - 1889) on the possibility of converting mechanical work into heat. The water in the jar will heat up. The effect is even more pronounced when the input and output of a home vacuum cleaner are “short-circuited”. But this is a risky demonstration, the temperature rises so rapidly that you may not have time to disconnect the “input” and “output”, which will lead to damage to the device.

The heater, the scheme of which is shown on, works approximately the same as the cooling system of an automobile engine, only the inverse problem is solved, not lowering the temperature, but increasing it. When the unit is started, the working fluid from the outlet hydrodynamic cavitation energy converter 3 through a pump 2 served along a short path to the entrance heat generator. After several circulations along the small (auxiliary) circuit, when the water reaches the set temperature, the second (working) circuit is connected. The temperature of the working fluid drops, but then, with well-chosen system parameters, it is restored to the required value.

Numerous designs of activators advertised by manufacturers, in fact, appear to be devices that impart kinetic energy to the working fluid. According to the authors of the projects, they succeed by using "special" design features heat generators and "non-traditional" physical effects to achieve high values ​​of efficiency h > 0.9. In some intriguing cases h, according to test results, exceeds unity. Explaining such unusual characteristics of well-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 fields arising from the rotational motion of the fluid.

As a rule, thermodynamic systems with cavitation heat generators as the initial source of mechanical energy, they have less often one, and more often two electric motors, which ensure the circulation of the coolant through the system and create conditions for maintaining hydrodynamic cavitation. In other words, electrical energy E1 with corresponding losses k1 converted into mechanical energy

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, (2)

where k2- coefficient of conversion (according to the terminology of the authors - transformation) of the mechanical energy of the coolant flow into its internal energy, and the value fluctuates, mostly from 0,9 before 4 . If the value k2 @ 0.9 with certain theoretical simplifications can be considered as high, but to some extent real, then the values k2 ≥ 1 require strong theoretical justification. The energy phenomenon is explained by the authors of the projects by the fact that their designs use a unique method of converting electrical energy into thermal energy through the use of “fluctuating vacuum under conditions of severe cavitation” and “energy of water molecules”.

Without touching further, for quite obvious reasons, torsion and thermonuclear problems, as well as the energy of the physical vacuum, let us consider some features of the use of 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 a phenomenon of the formation of a competitive phase in a continuous liquid in the form of cavities filled with working liquid vapor and dissolved gases.

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 in 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 occurrence of cavitation (hydraulic turbines, ship propulsion devices, pumps, agitators, technological installations), along with the results of theoretical studies, are supplemented by experimental data, which are based on modeling cavitation phenomena on special stands [ 4-7 ]. However, much is already known about cavitation. At least, by now, the main patterns associated with its occurrence and course have been established. Scientists and engineers have learned to quite successfully prevent destructive manifestations (for example, supercavitating ship propellers) and use them in technological processes when you need to destroy something, for example, particles of insoluble liquids, or organize chemical reactions that do not occur under normal conditions.

Researchers paid attention to the energy effects accompanying the appearance of a competitive phase in a liquid at pressures comparable to the pressure of saturated vapors of the working liquid. IN 1917 Lord Rayleigh solved the problem of the pressure developing in a liquid during the collapse of an "empty" spherical cavity [ 4 ]. For the case of spherical symmetry with an irrotational radial flow of fluid surrounding the cavity, the kinetic energy equation was obtained K L

, (3)

where p L is the density of the liquid, u- radial speed at an arbitrary distance r > R from the center of the cavity vr is the radial velocity of the cavity wall. In accordance with the theorem, the change in the kinetic energy of the liquid must be equal to the work done by the mass of the liquid when the cavity is closed

(4)

where is the pressure in the liquid at a distance, Rmax is the radius of the cavity at the moment of the beginning of its collapse, R0 is the final radius of the cavity. Equating ( 3 ) And ( 4 ), we can come to the equation for the velocity of the surface of a spherical cavity

. (5)

So, for example, for the case R max \u003d 10 -3 m And R 0 \u003d 10 -6 m at = 105 Pa, p L \u003d 103 kg / m 3 the velocity of the cavity wall is obtained 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 value of the kinetic energy of the liquid filling the cavitation cavity will be in accordance with the equation ( 3 ) value

, (6)

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

where s @ 4200 J/kg × K is the specific heat capacity 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 "cold" thermonuclear fusion reactions.

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Table 1

We should keep in mind that the calculations performed were obtained on the basis of a theory that allows an unlimited increase in pressure and velocity of the cavity boundaries at the final stages of closure in an ideal fluid with ultimate bulk strength z, the theoretical values ​​of which are given in Table. 1 .

Under the influence of pressures and temperatures, intermolecular distances in a liquid can change, and upon reaching a limit that is quite specific for each liquid, a discontinuity occurs. For example, for water, the intermolecular distance is L0 @ 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 the liquid, which is never observed in practice. If water had the specified strength, then get cavitation under the conditions of the devices under discussion would be impossible. In practice, under conditions of specially prepared portions of liquids that do not contain inhomogeneities, steam cores can arise due to thermal fluctuations. An increase in the volume of steam cores is possible if the pressure of saturated vapors of the liquid exceeds the external pressure, i.e.

, (9)

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

, (10)

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

the first term characterizes 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 R0, the third is the work required to fill the cavity with steam.
Thus, to create microinhomogeneities in a homogeneous liquid external forces some work must be done. In other words, the change in the state of the fluid, including the formation cavitation nuclei, is due to the supply of energy from external sources. The resulting 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 R0 and substitute this value in the condition ( 9 )

, (12)

where 1/t = dn 0 /dt, t- waiting time for discontinuity of a unit volume of liquid. Assuming that a single 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)

According to ( 12 ) the tensile strength for water is equal to z @ 1,6 × 10 8 Pa, almost two times less than the theoretical Kornfeld value 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. Flynn [ 6 ] measurements were published cavitation strength of distilled purified and tap water. When measuring the threshold values ​​of acoustic pressure at different frequencies, at which the occurrence of a competitive phase was recorded, the minimum pressure values ​​for untreated tap water were obtained. pr @ 5 × 10 4 Pa, and for distilled prepared water - pr @ 4 × 10 7 Pa.

Fig.3. Experimental thresholds for the occurrence of cavitation in water

The main reason for such a significant scatter cavitation the strength of water is its heterogeneity, i.e. presence in it cavitation nuclei filled with gas and liquid vapor, in other words, the emergence of a competitive phase occurs on the nuclei of critical radius already present in the liquid R r when they enter areas of low pressure.

If we assume that the process of core expansion proceeds according to the adiabatic scheme, then the relationship of the initial P G(0) and current P G the pressure of the gas in the 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 of the nuclei adjacent to the changing volume can be expressed by the following differential equation [ 5 ]

. (14)

For the maximum value of the radial velocity component, instead of the equation ( 5vr(max) @ 534 m/s, what in 26 times less, the hypothetical temperature gradient according to the equation ( 7 ) will be

,(16)

which is incommensurably less than the "fusion" temperatures mentioned in publications on cavitation heat generators. It should also be borne in mind that heating systems use ordinary tap water with a high level of gas content, in which relatively large Cavitation gas-filled cores. When such nuclei enter zones of low pressure, the nuclei will increase their volume to a certain maximum value, and then their volume will periodically change at their own frequency

. (18)

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

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

Thus, based on the analysis carried out, it can be concluded that under the conditions of heat generators, hydrodynamic cavitation cannot be considered as a source of additional energy. An ensemble of expanding, collapsing and pulsing cavitation The cavern is presented as a kind of energy energy transformer, the efficiency of which, in principle, like any transformer, cannot exceed one.

Literature

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

    Fridman V.M. Ultrasonic chemical equipment. - M.: Mashinostroenie, 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.

    Knapp R., Daly 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 book. Physical acoustics, // ed. W. Mason, T 1, - M .: Mir, 1967, S. 7 - 128.

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

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

 

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