Once Again on the Fundamental Law of Adiabatic Phase Formation

S. V. Polozhii

(Presented by the scientific seminar of the Department of TPP)

The main point in the reviews by ITMO of the Academy of Sciences of the BSSR and by the ITF of the Siberian Branch of the Academy of Sciences of the USSR on the application for the proposed discovery of the fundamental law of adiabatic phase formation (FL APF) is the denial of the novelty of the discovery of this law. In the ITMO review, the denial of the FL APF is carried out by substituting for the essence of the law of APF, its kinetics, and the principal propositions the known phenomena of phase transformations, and by invoking the existence of \(S\text{—}t\) and \(i\text{—}t\) diagrams of water vapor in order to determine the final result of the process of adiabatic phase formation. In the ITF review, the novelty of the FL APF is denied under the guise of its alleged lack of proof in the work, by means of arbitrary manipulations with the mathematical substantiation of this law in the work. In this way the principal proposition of the FL APF is denied: the simultaneity of the occurrence of two mutually opposite processes—adiabatic vaporization and adiabatic condensation, without heat exchange between the liquid and vapor phases as the pressure of a two-phase system is reduced.

The discovery of the fundamental law of adiabatic phase formation, set forth in the published works and in application OT-7343 [1, 2], leads to entirely new concepts and ideas about the physical essence and kinetics of adiabatic phase formation, and provides new quantitative and qualitative characteristics of APF in comparison with the present state of this question in world practice. For the first time, processes widely used in engineering (expansion of saturated and wet steam, outflow of heated water, etc.) are revealed as a single process of adiabatic phase formation, the final phase-forming effect of which is determined only by the initial state of the system: saturated water, steam, or a two-phase state.

A fundamentally new, previously unknown phenomenon proves to be the simultaneity of the occurrence of two mutually opposite processes: adiabatic vaporization and adiabatic condensation, regardless of the initial state of the system—saturated water, steam, or their mixtures in different proportions—with the same degree of intensity and in equal quantities under an isoentropic pressure drop per unit weight of the initial phase. Another, previously unknown property of the process of adiabatic phase formation is the conception of the causes of change in the aggregate state under isoen-

isotropic pressure release of saturated steam, water, or their mixtures, which exclude heat exchange between phases and the growth of one phase at the expense of the other; the temperature difference between the vapor and liquid phases in the process of adiabatic phase formation; and also independence of the change in the state of aggregation of each phase as the system pressure is released; an equal degree of intensity of vaporization and condensation in equal amounts per one and the same unit of weight of liquid and vapor, caused by the physical and thermodynamic properties of H₂O.

For the first time in the world, an explanation is given of the physical essence of the \(S—i\) diagram of H₂O as an equilibrium state obtained as a result of the action of the fundamental law of adiabatic phase formation for an adiabatic system. As a result of the action of the FL AP, when the pressure of saturated or wet steam is released at \(1 > X_0 > 0.5\), the final result under isoentropic pressure release is adiabatic condensation; under isoentropic pressure release of saturated water or wet steam at \(1 > Y_0 > 0.5\), adiabatic vaporization occurs. The continuous and independent course of two opposite processes under isoentropic pressure release of a two-phase system, \(X_0 = Y_0 = 0.5\), does not lead to a visible change in the phase-forming effect at any magnitude of pressure release—the change of one phase is fully compensated by the change of the other phase, \(AP = AK\), \(\Delta X = \Delta Y\), \(\Delta \Phi_{\mathrm{n}} = O\)—the isoentrope of equal phase formation.

For the first time, the quantitative and qualitative dependences and the driving forces of the process in adiabatic phase formation are clearly established and generalized (the initial state of the system, the magnitude, interval, and character of the pressure release), the phase-forming effect at the end of the process, the kinetic energy and dispersion of the flow; and a qualitative characteristic is also given of the dispersity of the flow as one of the most important properties of adiabatic phase formation and, in particular, the impossibility of growth of liquid droplets during the expansion of wet steam in a nozzle, the microdisperse structure of the flow at the outlet from nozzles as a consequence of the action of the FL AP: the simultaneous course of AC and AV with the same degree of intensity.

The discovery of the kinetics and physical essence of adiabatic phase formation fundamentally changes the ideas about these properties of AP that have become established in world practice. Modern conceptions of the processes of expansion of wet steam, the outflow of heated water, and the physical essence and kinetics of these processes are completely rejected. The concept of a one-sided direction of condensation of wet steam in the nozzles of steam turbines as a continuous process of growth of the liquid phase, the growth of individual liquid droplets as wet steam expands, proves to be incorrect. The concept of heat exchange between phases during the expansion of wet steam, the growth of liquid droplets at the expense of the transfer of heat from liquid to vapor in this process, which is the basis of the modern kinetics of the expansion of wet steam in steam-turbine nozzles [3, 4, 5], is excluded. Ideas about the presence of a temperature difference between liquid droplets and vapor during its expansion, about a higher temperature of the droplets than of the vapor, introduced to determine the growth of liquid droplets by heat-exchange equations, prove to be erroneous. Modern ideas about inversion of the state of aggregation during the expansion of wet steam, theoretically substantiating the one-sided direction of the condensation process on the basis of heat exchange between phases and the presence of a temperature difference between liquid and vapor, prove to be untenable. Theoretical constructions for estimating qualitative and quantitative

characteristics during the expansion of wet steam and the outflow of heated water, and the interpretation of these processes in the scientific and technical literature in our country and abroad. For the first time, the reasons for such an unsatisfactory state in the science and practice of using adiabatic phase formation in all countries over many decades are revealed [1, 2]. Also for the first time in world practice, the erroneous nature is revealed of the methods of experimental and theoretical studies of moisture losses in steam turbines, of the physical ideas about the kinetics of this process in steam-turbine nozzles, of the physical model and mechanism of moisture losses, of the dispersity and structure of the flow, and of the mathematical apparatus and dependences for calculating moisture losses and the quantitative and qualitative characteristics of a two-phase flow in steam-turbine nozzles. This constitutes the worldwide novelty of the discovery of the fundamental law of adiabatic phase formation, its importance for scientific and practical purposes, for solving problems connected with increasing the efficiency of wet-steam turbines and introducing adiabatic phase formation into power engineering [6, 7].

Another fundamentally important point is the discovery of adiabatic phase formation as a natural process of nature. The review of the ITF SB AS gives considerations for not recognizing AP as a natural process of nature. As the first argument, the proposition is advanced that the equality \(S'_0 - S'_1 = S''_0 - S''_1\) is inapplicable to all substances of nature, “which can be used for a narrow range of substances and for this reason cannot be treated as a law valid for all substances occurring in nature.”

The failure of this law to correspond fully to all substances in nature does not deprive the properties and basic propositions of the AP process for \(\mathrm{H_2O}\) of their force; they are objective independently of other substances, they characterize a specific substance of nature, and for this reason it is impossible to deny the FL of AP for \(\mathrm{H_2O}\). The laws of nature are objective and concrete. For example, the phenomenon of magnetism, its properties and laws are inherent in some metals and unsuitable for other metals and substances of nature.

The FL of AP has been discovered and reflects the process of adiabatic phase formation for \(\mathrm{H_2O}\) in the form of saturated steam, water, and the two-phase state: saturated water—steam. It is not applicable to all substances of nature, which have different properties and structures.

Nature possesses enormous sources of highly compressed heated water and saturated steam, at whose exit to the surface the natural process of adiabatic phase formation is realized, with manifestation of the fundamental law and properties of this process—the formation of a new phase, the kinetic energy of the flow, and the dispersity of the liquid phase. Another motivation for not recognizing adiabatic phase formation as a natural process of nature in the ITF review is the reference to the absence of an isentropic process in nature, for which the formulation and theoretical substantiation of the fundamental law of AP are given. In technical installations and under natural conditions, adiabatic phase formation proceeds only with a certain approximation to the isentropic process. This proposition likewise cannot serve as an argument for denying this natural phenomenon.

Deviation of the AP process from the isentropic one in technical installations or under natural conditions leads to a change in the energetic and phase-forming effect, but does not alter the physical essence of the AP process. These deviations are amenable to calculation and can always be taken into account. The discovery of the FL of AP made it possible for the first time to decipher the physical essence of a geyser, or steam “fountain,” as a process of adiabatic

phase formation—adiabatic vapor formation or adiabatic condensation, and also to determine the phase state of the deep source of this natural phenomenon. In this respect, the discovery of the FLA PhF and the discovery of APF under natural conditions has not only cognitive significance, but also practical significance—for determining the phase and energy characteristics of underground APF sources. From the phase-forming effect of geysers (wells), the kinetic energy of the flow, and the pressure of the underground source, one can determine the phase state and the specific energy potential of the source.

The formulation of the FLA PhF for the isoentropic process of APF of H₂O corresponds, to a high degree of approximation, to real processes in the expansion of wet steam in the nozzles of steam turbines and especially in specially designed laboratory installations, and makes it possible to take into account the limiting degree of perfection of this natural process, as well as to substantiate theoretically the physical essence and kinetics of adiabatic phase formation.

The ITMO of the Academy of Sciences of the BSSR also took the position of not recognizing the novelty of the discovery of the FLA PhF, replacing the essence of this law with the known character of the phenomena of phase transformations under adiabatic change of the state of water, steam, or their mixture (the use of this process in thermal power engineering during the expansion of wet steam in steam turbines, in obtaining steam from blowdown water, for desalination of seawater, drying of solutions, etc.), and also with the existence of \(S—t\) and \(S—i\) diagrams for water vapor and courses in technical thermodynamics published during the last decade. Such nonrecognition of the FLA PhF and its novelty is either a deliberate distortion of the materials of the GPI investigations or an unserious attitude toward consideration of this question.

In courses of technical thermodynamics there is no notion not only of the FLA PhF, but also of the very process of adiabatic phase formation as a specific phenomenon. Moreover, in courses of technical thermodynamics a theoretical basis has been developed for the modern incorrect conception of these phenomena; theoretical proofs are given for the formation of only one phase in this process, of heat exchange between phases, and of the presence of a temperature difference between the vapor and liquid phases—everything that is denied by the FLA PhF. In the thermal diagrams considered in courses of technical thermodynamics, the process of adiabatic phase formation is described only as a one-sided process: either only condensation when the pressure of saturated steam is reduced (the right-hand part of the \(S—t\) diagram), or only vapor formation when the pressure of saturated water is reduced along the entire path from the initial to the final state. For the same purpose, the concept and theoretical proofs of the “inversion” of the aggregate state have been introduced into modern thermodynamics: the formation of only one phase—either liquid or vapor.

Another feature of the denial of the FLA PhF and of its substantiation is the use of incorrect methods and devices in the conclusions of the ITMO and ITF. In the review of the ITMO of the Academy of Sciences of the BSSR, an error was declared in one of the basic formulas by which the final phase-forming effect is determined in the isoentropic pressure drop of saturated steam (I). Instead of this formula (I),

\[ Y_2=\frac{(S''_2-S''_1)\cdot T_{\mathrm{н}2}}{r_2} \tag{I} \]

after a number of mathematical calculations, another formula was proposed in the review, allegedly more accurate and correct.

\[ Y_2=(1-X_2)=-\frac{(S'_2-S'_1)\cdot T_{\mathrm{н}2}}{r_2} +\left(1-\frac{r_1\cdot T_{\mathrm{н}2}}{T_{\mathrm{н}1}\cdot r_2}\right). \tag{II} \]

However, it proved paradoxical that this new formula (II) gives the same results as formula (I). Both formulas correctly and accurately describe the process in the final state of APF.

In the review by the Institute of Thermophysics, Siberian Branch, USSR Academy of Sciences, in order to refute the theoretical proofs of the FLAW of APF in the application, the physical essence and kinetics of APF from the complex of interrelated formulas (1), (2), (3), (4)—

\[ (X_0-\Delta Y)+(Y_0-\Delta X)=1 \tag{1} \]

\[ \Delta X=\frac{(S'_0-S'_1)\cdot T_{\mathrm{н}1}}{r_1}\cdot Y_0 \tag{2} \]

\[ \Delta Y=\frac{(S''_0-S''_1)\cdot T_{\mathrm{н}1}}{r_1}\cdot X_0 \tag{3} \]

\[ X_1+Y_1=1 \tag{4} \]

—were arbitrarily discarded: formulas (2) and (3), which describe the increment of the new phase during the isoentropic expansion of wet steam. Then, comparing formulas (1) and (4), and taking as the basis the modern scheme of the APF process as a process in which the growth of one phase occurs at the expense of the decrease of the other phase, they expressed the change of phases through the initial and final static state of the system: \(\Delta Y=Y_1-Y_0\), \(\Delta X=X_1-X_0\). Taking into account that for any state of wet steam under equilibrium conditions \(Y_1+X_1=1\), they came to the conclusion that, during the expansion of wet steam, the increment of one phase is always equal to the loss of the other phase, \(\Delta X=-\Delta Y\) (either only condensation of steam occurs, or only vaporization), and on this basis declared erroneous and unproven the simultaneous occurrence of two opposite processes—one of the main propositions of the FLAW of APF. Formulas (1) and (4), without the dependencies (2) and (3), do not characterize the process (kinetics) of adiabatic phase formation. They reflect the thermodynamic state of wet steam for any two arbitrary states of points of the \(S-t\) diagram, irrespective of the path by which these thermodynamic states in the diagram were reached. In processes of phase transitions with heat exchange with the external medium and a static position of the system determined by constant pressure, an ordinary process of formation of one phase at the expense of another takes place, \(\Delta X=-\Delta Y\), up to the complete transformation of one phase into the other. In an isolated system without heat exchange with the external medium, when the pressure of the system is dropped—for example, during the expansion of wet steam in turbines—the formation of one phase at the expense of the other and the transfer of heat from one phase to the other are impossible, since in such a scheme these processes turn out not to be connected with the conversion of part of the system’s energy into the kinetic energy of the flow. Under such a scheme the energy balance of the system is violated: the loss of heat of one phase is completely received by the other phase, and the first law of thermodynamics and the law of the corresponding state of the system are violated. Therefore, according to such a “theory,” in an isoentropic pressure drop of wet steam, the different phase-forming effect produced by changing the initial state of the system from \(X_0=1\) to \(X_0=0\), with one and the same magnitude of the pressure drop \(\Delta P\) and unchanged thermodynamic and physical parameters of the liquid and vapor phases—\(P_0\), \(t_0\), \(i'_0\), \(i''_0\), \(S'_0\), \(S''_0\), \(r_0\), \(C'_0\), \(C''_0\), \(\sigma_0\)—is completely inexplicable.

The denial of the validity of the equality

\[ S'_0-S'_1=S''_0-S''_1 \]

in the isoentropic pressure drop of saturated or wet steam, which is laid as the basis of the theoretical proof of the FLAW of APF, is unlawful. This denial in the review of the Institute of Thermophysics, Siberian Branch, USSR Academy of Sciences, is built—

but on the assumption that there is heat exchange between the phases, by replacing the amount of heat transferred from one phase to the other through entropy with the determination of this heat through the heat capacity, \(T dS' = C' dT\) and \(T dS'' = C'' dT\), for an elementary change in the saturation temperature. Then the equality \(dS' = dS''\) is possible only if the heat capacities of the saturated liquid \(C'\) and of the saturated vapor \(C''\), which at one and the same pressure cannot be equal, are equal. Such a proof would be valid if heat exchange between the phases actually existed in the process of APF.

The energy efficiency of adiabatic phase formation, for an unchanged magnitude and interval of the isoentropic pressure drop, like the phase-forming effect, is wholly determined by the initial ratio of the liquid and vapor phases. The kinetic energy of the flow is the total result of the formation of the kinetic energy of each phase (Table 1). The heat drop during the pressure drop of the vapor phase upon its condensation

Table 1

\[ H_x = \{ i_0'' - [i_1'' + (S_0'' - S_1'') \cdot T_{\mathrm{sat}}] \} \cdot X_0 . \]

The heat drop of the liquid phase upon its evaporation

\[ H_y = \{ i_0' - [i_1' + (S_0' - S_1') \cdot T_{\mathrm{sat}}] \} \cdot Y_0 . \]

The resulting heat drop of adiabatic phase formation is \(H_{\mathrm{AF}} = H_x + H_y\). In this case all the thermodynamic and physical parameters and characteristics of the vapor and liquid phases remain unchanged:

\[ p_0, p_1, \Delta p; \quad t_0, t_1, \Delta t; \quad i_0', i_1', i_0'', i_1''; \quad S_0', S_1', S_0'', S_1''; \quad C_0', C_0'', C_1', C_1'' . \]

Recognition of the fundamental law of adiabatic phase formation is necessary for fundamental changes in studies of the gas dynamics of two-phase media, the theory of wet-steam turbines [3, 4, 5], and in other cases where adiabatic phase formation is used or manifests itself.

References

1. S. V. Polozhii. On the question of the kinetics of the condensation process in a turbine stage. Proceedings of TPI. Vol. 137, 1965.

1. S. V. Polozhii. Adiabatic phase formation. TPI Information Bulletin on the problem of converting thermal power plants to adiabatic phase formation, 1969, No. 4. State registration No. 70002200. Microfilm, Moscow, 1970.

2. M. E. Deich, G. A. Filippov. Gas dynamics of two-phase media. Moscow, “Energiya,” 1968.

3. I. I. Kirillov, R. M. Yablonik. Fundamentals of the theory of wet-steam turbines. Leningrad, “Mashinostroenie,” 1968.

4. M. D. Vaisman. Thermodynamics of vapor–liquid flows. Moscow, “Energiya,” 1967.

5. S. V. Polozhii. Review of TPI studies on steam-turbine installations with adiabatic phase formation. Questions of converting thermal power plants to APF. TPI Information Bulletin on the problem of converting thermal power plants to APF, 1970, No. 5. State registration No. 70013070. Microfilm, Moscow, 1970.

6. S. V. Polozhii. On the methodology of experimental studies of losses due to moisture in steam turbines. “Izvestiya TPI,” vol. 205, 1972.