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ON THERMAL CAPACITY OF HYDRODYNAMIC CAVITATION

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The report presents some energy aspects that accompany the operation of cavitation heat generators , widely advertised as highly effective sources of thermal energy . It is shown, in particular, that the occurrence of ultrahigh temperature and pressure gradients is possible only in specially prepared "pure" homogeneous liquids. In conditions of "technical" used in heating systems, the effects declared by the authors of the projects are fundamentally impossible.

Recently, in scientific and technical publications of a popular and information orientation, including the Internet, hydrodynamic devices are widely advertised , intended, 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 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 [1]

In Fig. 1 , as an example, is a schematic diagram of a boiler house, the active element of which is a rotary cavitational heat generator , which is represented as a new generation of thermal machines that convert mechanical, electrical and acoustic effects on liquid into heat.

The increase in the temperature of the coolant occurs, in the opinion of the authors, due to the following effects: the conversion of mechanical energy due to internal friction arising when the coolant moves; Transformation of electrical energy into thermal energy due to electro-hydraulic effect and heating of thermal elements; Hydroacoustic energy into thermal energy due to cavitation and vortex effects . In the scheme of Fig. 2, the authors of [ 1 ] adopted the following designations: 1 - electric motor, 2 - cavitation heat generator, 3 - pressure gauge, 4 - boiler, 5 - air cock, 6 - hot water supply pipe, 7 - temperature sensor, 8 - automatic block 9 - heat exchanger, 10 - heating radiator, 11 - expansion tank, 12 - filter for cleaning the coolant, 13 - circulating pump.

Thus, the main element of the scheme is the cavitational heat generator 2 , which in this case is a rotary-type apparatus that is widely used in the chemical industry (for example, rotary devices of the GART class [ 2 ]). In addition to rotary apparatus, at present, attempts are being actively promoted and attempts are being made to scientifically substantiate the high energy indices of vortex devices designed on the basis of Rank's tube [ 3 ].

Systems of cavitation heat generators , in spite of the most diverse names (the apparently second terminology seems to have not yet been negotiated) consists of four main elements ( Figure 2 ): the driving motor 1, the pump 2, the actual cavitation heat source 3 through which the transformation Mechanical energy into thermal energy and a consumer of thermal energy 4.

Fig. 2. Typical Block Diagram of a Cavitation Heat Generator

The elements of the simplified structural diagram 2 are standard, practically, for any hydraulic system intended for the transport of liquid or gas.

The principle of operation of such energy transformers can be observed using the example of a public pump for watering beds and lawns in country areas. It is necessary to fill with water the usual three-liter jar and force the pump to take water from the jar and drop it there. After 5 - 10 minutes you can be convinced of the correctness of James Prescott Joule (1818 - 1889) about the possibility of converting mechanical work into heat. The water in the jar heats up. The effect is even brighter when the home vacuum cleaner's input and output are " closed ". But this is a risky demonstration, the temperature is rising so rapidly that you can not have time to separate the "input" and "exit", which will lead to damage to the device.

The heater, the circuit of which is shown in Fig. 2 works in much the same way as the cooling system of an automobile engine, only the reverse task is solved, not the temperature drop, but its increase. When the unit is started, the working fluid from the output of the hydrodynamic cavitation energy converter 3 via the pump 2 is fed along a short path to the heat generator inlet. 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 chosen parameters of the system, is restored to the required value.

Numerous designs of activators advertised by manufacturers, in fact, are represented by devices that communicate the working fluid kinetic energy. According to the authors of the projects, they manage to achieve high efficiencies h> 0.9 by using "special" design features of heat generators and " non-traditional " physical effects. In a number of intriguing cases, h , according to the 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 the " cold " thermonuclear fusion) or torsion fields arising during the rotational motion of a liquid.

As a rule, thermodynamic systems with cavitational heat generators as the initial source of mechanical energy are less often one, and more often - two electric motors that circulate the coolant through the system and create conditions for maintaining hydrodynamic cavitation. In other words, the electric energy E1 with the corresponding losses k1 is converted into mechanical energy

, (2)

Where k ₂ is the coefficient of transformation (in the terminology of the authors - the transformation) of the mechanical energy of the coolant flow into its internal energy, and the value varies, most of it from 0.9 to 4 . If the value of k ₂@ 0.9 for certain theoretical simplifications can be regarded as high, but to some extent real, then the values ​​of 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 method of converting electrical energy into thermal energy by using a "fluctuating vacuum in the conditions of rigid cavitation" and "energy of water molecules".

Without further mentioning, for 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-exchange processes. The processes of boiling, acoustic and hydrodynamic cavitation can be represented as the phenomenon of formation in a continuous liquid of a competitive phase in the form of cavities of a working fluid filled with steam 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 in cavitation processes agree that the phenomenon in some of its manifestations is not yet predictable. The parameters of engineering structures and devices, whose operation is associated with the occurrence and flow of cavitation (hydro turbines, ship propulsors, pumps, mixing devices, process units), along with the results of theoretical studies, are supplemented by experimental data, based on simulation of cavitation phenomena at special stands [ 7 ]. At the same time, much is already known about cavitation. At least, by now, the main regularities associated with its occurrence and progress have been established. Scientists and engineers have learned to successfully prevent destructive manifestations (for example, supercavitating ship propellers) and use them in technological processes when it is necessary to destroy something, for example particles of insoluble liquids, or to organize chemical reactions that do not occur under normal conditions.

The energy effects accompanying the appearance of a competitive phase in a liquid under conditions of pressures commensurate with the pressure of saturated vapors of a working fluid have attracted attention long ago. In 1917, Lord Rayleigh solved the problem of the pressure developing in a liquid when an "empty" spherical cavern collapsed [ 4 ]. For the case of spherical symmetry in the irrotational radial flow of a fluid surrounding the cavity, the kinetic energy equation K _L

, (3)

Where p _L is the density of the fluid, u is the radial velocity at an arbitrary distance r> R from the center of the cavity, v _r is the radial velocity of the cavity wall. In accordance with the theorem, the change in the kinetic energy of the liquid should be equal to the work done by the mass of the fluid when the cavity is closed

(4)

Where - pressure in the liquid at a distance , _Rmax is the radius of the cavity at the moment of the beginning of its collapse, and R ₀ is the final radius of the cavity. Equating ( 3 ) and ( 4 ), one can arrive at the equation of the velocity of motion of the surface of a spherical cavity

. (5)

So, for example, for the case of R _max = 10 ^-3 m and R ₀ = 10 ^-6 m at = 105 Pa , p _L = 103 kg / m ^{3, the} velocity of the wall of the cavity 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 magnitude of the kinetic energy of the fluid filling the cavitation cavity will, in accordance with equation ( 3 ), amount to

, (6)

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

, (7)

Where c @ 4200 J / kg × K is the specific heat of water. It is natural to assume that at such high temperatures, processes at the molecular and atomic levels are possible. It must be assumed that it was precisely these results of calculations that led the designers of cavitation heat generators to the hypothesis of the possibility of reactions of "cold" thermonuclear fusion.

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 in practice is never observed. If water had this strength, then it would be impossible to get cavitation in the conditions of the devices under discussion. In practice, in the conditions of specially prepared portions of liquids that do not contain inhomogeneities, the steam nuclei can arise as a result of thermal fluctuations. An increase in the volume of steam nuclei is possible if the pressure of saturated vapor of the external pressure liquid exceeds the pressure, i.e.

, (9)

Where p _sp is the saturated vapor pressure of the liquid, s _{L / sp} is the surface tension coefficient 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 Ya. Zeldovich [ 5 ]

, (10)

Where n ₀ - number of nuclei formed, F - constant factor, k _B @ 1.4 × 10 ^-23 J / K - Boltzmann constant, T - absolute temperature, A (R ₀ ) - nucleation formation work

, (eleven)

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 radius R ₀ , the third is the work necessary to fill the cavity with steam.
Thus, in order to create microinhomogeneities in a homogeneous liquid by external forces, a certain work has to be done. In other words, the change in the state of the fluid, including the formation of cavitation nuclei, occurs as a result of the supply of energy from external sources. The resulting cavitation core can increase or decrease its volume depending on the ratio of the external pressure and the vapor pressure inside the nucleus. The kernel growth condition can be obtained by combining equations ( 11 ) and ( 10 ), i.e. From the equation ( 11 ) determine the value of R ₀ and substitute this value into the condition ( 9 )

, (12)

Where 1 / t = dn ₀ / dt , t is the waiting time for discontinuity discontinuity of the unit volume of the liquid. Assuming that a single cavitation nucleus in a volume of 1 cm ^{3 is} formed within one second and taking, according to Kornfeld, A @ 10 ^{3 1} s ^{- 1} m ^{3 is} obtained

In this case

.(12)

In accordance with ( 12 ), the tensile strength for water is z = 1.6 × 10 ⁸ Pa , almost half the theoretical value of Kornfeld and three times smaller than the molecular equation ( 8 ).

As established experimentally [ 4 ± 7 ], the cavitation strength of liquids is several orders of magnitude lower than the theoretical values. For example, M.G. Sirotyuk [ 7 ] and G. Flyn [ 6 ] published data on measurements of cavitation strength of distilled purified and tap water. When measuring the threshold values ​​of the acoustic pressure at different frequencies at which the emergence of the competitive phase was recorded, the minimum pressure values ​​for untreated tap water p _{c r} @ 5 × 10 ⁴ Pa were obtained, and for distilled prepared water - p _{c r} @ 4 × 10 ⁷ Pa .

Fig.3. The experimental thresholds of cavitation in water [6, 7]

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

If we assume that the expansion of the nucleus proceeds according to the adiabatic scheme, then the relationship between the initial gas pressure P _{G (0)} and the current gas pressure P _G in the increasing volume of the nucleus can be represented on the basis of the Poisson equation can be represented as follows

, (13)

Where g is the adiabatic exponent. In this case, the kinematic parameters of the nucleus adjacent to the volume 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 equation ( 5 ), we need to write the following relation, which is the first integral of equation ( 14 )

. (15)

Taking = 105 Pa , p _G(0) @ 1 × 10 ³ Pa , the maximum value of the velocity is v _{r (max)}@ 534 m / s , which is 26 times less, the hypothetical temperature gradient in accordance with equation ( 7 ) will be

,(16)

Which is incommensurably less than the "thermonuclear" temperatures, which are mentioned in the publications devoted to cavitation heat generators . It should also be borne in mind that in heating systems, conventional tap water with a high level of gas content is used, in which there are certainly relatively large cavitation gas-filled nuclei. When such nuclei hit lower pressure zones, 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 of thermal energy not exceeding 1% of the total energy of the cavity.

It should be borne in mind that the hydrodynamic systems of cavitation heat generators are closed ( Figure 2 ), which presupposes the presence of a circulating circuit. The liquid that has passed the zone of low pressures in the heat generator again gets there after a short time. Such fluid circulation through the cavitation zone is characterized by hysteresis phenomena [ 8 ], when the number and size distribution of the cavitation nuclei changes. The cavitation strength of the liquid drops, 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 carried out, it can be concluded that under the conditions of heat generators, hydrodynamic cavitation can not be regarded as a source of additional energy. The ensemble of expanding, collapsing and pulsing cavitation caverns is presented as a kind of energy transformer of energy whose efficiency, in principle, like any transformer can not exceed unity.

Literature

1. Http://www.tstu.ru/structure/kafedra/doc/maxp/eito6.doc
2. Fridman V.M. Ultrasonic chemical apparatus. - M .: Mechanical Engineering, 1967. - 211 p.
3. Потапов Ю.С., Фоминский Л.П., Вихревая энергетика и холодный ядерный синтез с позиций теории движения. - Кишинев – Черкассы: ОКО-Плюс. ,2000. - 387 с.
4. Кнэпп Р., Дейли Дж., Хэммит Ф. Кавитация. - М.: Мир, 1974. - 678 с.
5. Перник А.Д. Проблемы кавитации. - Л.: Судостроение, 1966. - 435 с.
6. Флин Г. Физика акустической кавитации в жидкостях. В кн. Физическая акустика, // под ред. У. Мэзона, Т 1, - М.: Мир, 1967, С. 7 - 128.
7. Сиротюк М.Г. Экспериментальные исследования ультразвуковой кавитации. В кн. Мощные ультразвуковые поля, // под ред. Л.Д. Розенберга, 1968. С. 168 - 220.
8. Васильцов Е.А., Исаков А.Я. Гистерезисные свойства кавитации // Прикладная акустика. Issue. 6. -Таганрог: ТРТИ, 1974. -С.169-175.

print version
Автор: Исаков Александр Яковлевич
Почтовый адрес: Г. Петропавловск-Камчатский, ул. Ключевская 35, КамчатГТУ,
Телефон: первому проректору, сл. телефон 423 501, дом. Tel. 426 990
Дата публикации 05.10.2006гг

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