Abstract
The specific feature of the study of the dynamics of vapor bubbles during boiling of a liquid in a centrifugal force field is the fact that the velocity of a bubble is much greater than the rate of change of its radius, and its movement occurs in fields of variable pressure and underheating that have to be determined in the solution of the problem. In addition, when investigating processes occurring when liquid helium boils in a centrifugal force field, its thermodynamic parameters may be close to the critical values, and the dependences of the thermophysical properties of the liquid and vapor on the temperature and pressure must be taken into consideration. The equation of state of a substance close to its critical thermodynamic point cannot be an approximation to the equation of state of an ideal gas, as has been suggested in a series of articles. The nonequilibrium nature of the phase transition must be taken into consideration in the case of substances existing at near-critical parameters and substances with a low coefficient of accommodation. A marked deformation of the bubbles, which also has to be taken into account, will be observed in strong centrifugal force fields. Such studies have not appeared in the specialist journals. Equations of the two-temperature and two-velocity hydrodynamics of two-phase media in a one-dimensional form for substances obeying the equation of state for an ideal gas were discussed in [1, 2] with allowance for the dependence of the thermophysical properties on the temperature and pressure. In strong centrifugal force fields the one-dimensional approach is unacceptable and the flow of liquid around a buoyant bubble must be taken into account. A joint examination of the change in the temperature field with time in the vicinity of a vapor bubble with changes in its dimensions and position was made for the first time in [3–8]. The present article is an extension of the latter work and takes the aforementioned factors into account.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
R. I. Nigmatulin, Principles of the Mechanics of Heterogeneous Media [in Russian], Nauka, Moscow (1978).
R. I. Nigmatulin, P. S. Khabeev, and F. B. Nagiev, “Heat transfer of a disintegrating and condensing vapor bubble,” in: Heat Transfer and the Hydrogasdynamics of Boiling and Condensation. Proc. 21st Siberian Seminar on Thermophysics, Novosibirsk, 1978, Novosibirsk (1979), pp. 22–27.
P. S. Chernyakov and Yu. A. Kirichenko, “Dynamics of spherical bubbles in a superheated liquid at small Reynolds numbers,” in: Problems of Hydrodynamics and Heat Transfer in Cryogenic Systems, No. 3 [in Russian], Khar'kov (1973), pp. 81–86.
Yu. A. Kirichenko and P. S. Chernyakov, “Dynamics of spherical bubbles in a superheated liquid at large Reynolds numbers,” in: Problems of Hydrodynamics and Heat Transfer in Cryogenic Systems, No. 3 [in Russian], Khar'kov (1973), pp. 74–80.
D. D. Wittke and B. T. Chao, “Collapse of vapor bubbles with translatory motion,” Trans. ASME, Ser. C, J. Heat Transfer,89, 19 (1967).
Yu. A. Kirichenko, A. V. Krytov, and P. S. Chernyakov, “Dynamics of spherical vapor bubbles in a superheated liquid,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 1, 54 (1977).
P. S. Chernyakov, “Velocity and temperature fields in liquid flow around spherical vapor bubbles in a superheated liquid,” Inzh.-Fiz. Zh.,43, 670 (1982).
Yu. A. Kirichenko, P. S. Chernyakov, and V. E. Seregin, “Vapor phase motion in cryogenic systems containing sur rheated and subcooled liquids,” Cyogenics,23, 15 (1983).
J. F. Harper, “The motion of bubbles and drops through liquids,” Adv. Appl. Mech.,12, 59 (1972).
R. D. McCarty, “Thermodynamic properties of Helium-4 from 2 to 1500 °K at pressures to 108 Pa,” J. Phys. Chem. Ref. Data,2, 923 (1973).
V. V. Sychev, A. D. Vasserman, A. D. Kozlov, G. A. Spiridonov, and V. A. Tsymarnyi, Thermodynamic Properties of Nitrogen [in Russian], Izd. Standartov, Moscow (1977).
V. A. Akulichev, Cavitation in Cryogenic and Boiling Liquids [in Russian], Nauka, Moscow (1978).
Yu. A. Kirichenko, P. S. Chernyakov, and V. E. Seregin, “Calculation of the thermodynamic parameters of helium in a centrifugal force field,” Cryogenics,22, 395 (1982).
J. Siekmann and K. Dittrich, “Über die Bewegung von Gasblasen in einem rotierenden Medium,” Ingenieur Archiv.,44, 131 (1975).
I. Catton and S. Schwartz, “Motion of bubbles in a rotating container,” J. Spacecr. Rockets,9, 468 (1972).
Yu. A. Kirichenko and P. M. Levchenko, “Investigation of the internal characteristics of boiling of cryogenic liquids,” Preprint No. 22 [in Russian] (1977).
W. A. Beckman and T. Merle, “A photographic study of boiling in an accelerating system,” Trans. ASME, Ser. C, J. Heat Transfer,87, 305 (1965).
I. S. Riman and R. L. Kreps, “Added masses of bodies of various shapes,” Tr. TsAGI, No. 635, 45 (1974).
A. A. Samarskii, Theory of Difference Schemes [in Russian], Nauka, Moscow (1977).
B. M. Berkovskii and E. F. Nogotov, Difference Methods for Investigating Problems of Heat Transfer [in Russian], Nauka i Tekhnika, Minsk (1976).
W. E. Milne, Numerical Solution of Differential Equations, New York (1953).
Author information
Authors and Affiliations
Additional information
Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 66–71, July–August, 1984.
Rights and permissions
About this article
Cite this article
Kirichenko, Y.A., Seregin, V.E. & Chernyakov, P.S. Method for calculating the dynamics of vapor bubbles when a liquid boils in a centrifugal force field. Fluid Dyn 19, 569–574 (1984). https://doi.org/10.1007/BF01091078
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01091078