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Waves in liquids with vapour bubbles

Published online by Cambridge University Press:  21 April 2006

R. I. Nigmatulin ,
N. S. Khabeev  and
Zuong Ngok Hai
R. I. Nigmatulin
Affiliation:
Institute for North Development Problems, Siberian Branch of the USSR Academy of Sciences, 625003, Tyumen, box. 2774, USSR
N. S. Khabeev
Affiliation:
Institute of Mechanics, M.V. Lomonosov Moscow University, Moscow V-234, USSR
Zuong Ngok Hai
Affiliation:
Institute of Mechanics, The National Centre for Scientific Research of the Socialist Republic of Vietnam, Hanoi
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Abstract

An investigation of wave processes in liquids with vapour bubbles with interphase heat and mass transfer is presented. A single-velocity two-pressure model is used which takes into account both the liquid radial inertia due to medium volume changes, and the temperature distribution around the bubbles. An analysis of the microscopic fields of physical parameters is aimed at closing the system of equations for averaged characteristics. The original system of differential equations of the model is modified to a form suitable for numerical integration. An elliptic equation is obtained to determine the field of the mixture average pressure at an arbitrary time through the known fields of the remaining quantities. The existence of the steady structure of shock waves, either monotonic or oscillatory, is proved. The effect of the initial conditions, shock strength, volume fraction, and dispersity of the vapour phase and of the thermophysical properties of the phases on shock-wave structure and relaxation time is studied. The influence of nonlinear, dispersion and dissipative effects on the wave evolution is also investigated. The shock adiabat for reflected waves is analysed. The results obtained have proved that the interphase heat and mass transfer determined by the thermal diffusivity of the liquid greatly influences the wave structure. The possible enhancement of disturbances in the region of their initiation is shown. The model has been tested for suitability and the results of calculations have been compared with experimental data.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 186 , January 1988 , pp. 85 - 117
Copyright
© 1988 Cambridge University Press

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References

Aidagulov, R. R., Khabeev, N. S. & Shagapov, V. Sh. 1977 Structure of the shock wave in a liquid with gas bubbles with allowance for unsteady interphase heat transfer. Zh. Prikl. Mekh. Tekh. Fiz. 3, 67–74.Google Scholar
Azamatov, A. Sh. & Shagapov, V. Sh. 1981 Propagation of small perturbations in a vapour–gas–liquid medium. Akust. Zh. 27, 161–169.Google Scholar
Batchelor, G. K. 1969 Compression waves in a suspension of gas bubbles in liquid. In Fluids Dynamics Transactions, vol. 4. (ed. W. Fiszdon, P. Kucharczyk & W. I. Prosnak), p. 425. Warszawa: PWN.
Berezin, Yu. A. & Karpman, V. I. 1966 On nonlinear evolution of perturbations in plasma and other dispersion media. Zh. Exp. Theor. Fiz. 51, 1557–1568.Google Scholar
Borisov, A. A., Gel'Fand, B. E., Gubaidullin, A. A., Gubin, S. A., Gubanov, A. V., Ivandaev, A. I., Nigmatulin, R. I., Filin, N. V., Timofeev, E. I. & Khabeev, N. S. 1977 Enhancement of shock waves in liquids with vapour bubbles. In Nonlinear Wave Processes in Two-Phase Media (ed. S. S. Kutateladze), pp. 67–73. Institute of thermal physics, SD of Academy of Sciences of the USSR, Novosibirsk.
Borisov, A. A., Gel'Fand, B. E., Nigmatulin, R. I., Rakhmatulin, Kh. A. & Timofeev, E. I. 1982 Enhancement of shock waves in liquids with bubbles of vapour and soluble gas. Dokl. Akad. Nauk SSSR 263, 594–598.Google Scholar
Campbell, L. I. & Pitcher, A. S. 1958 Shock waves in a liquid containing gas bubbles. Proc. R. Soc. Lond. A 243, 534–545.Google Scholar
Carslaw, H. S. & Jaeger, J. C. 1959 Conduction of Heat in Solids, 2nd edn. Clarendon.
Chapman, R. B. & Plesset, M. S. 1971 Thermal effects in the free oscillation of gas bubbles. Trans. ASME D: J. Basic. Engng 93, 373–376.Google Scholar
Deksnis, B. K. 1978 Propagation of moderately strong shock waves in a two-phase medium. Izv. I Akad. Nauk Latv. SSR, Ser. Fiz. Tekh. 1, 73–81.Google Scholar
Drumheller, D. S., Kipp, M. E. & Bedford, A. 1982 Transient wave propagation in bubbly liquids. J. Fluid Mech. 119, 347–365.Google Scholar
Gel'Fand, B. E., Gubin, S. A., Kogarko, B. S. & Kogarko, S. M. 1973 Investigation of compression waves in a mixture of a liquid and gas bubbles. Dokl. Akad. Nauk SSSR 213, 1043–1046.Google Scholar
Gel'Fand, B. E., Stepanov, V. V., Timofeev, E. I. & Tsyganov, S. A. 1978 Enhancement of shock waves in a nonequilibrium system ‘liquid-soluble gas bubbles’. Dokl. Akad. Nauk SSSR 239, 71–74.Google Scholar
Gubaidullin, A. A., Ivandaev, A. I. & Nigmatulin, R. I. 1976 Unsteady waves in a liquid with gas bubbles. Dokl. Akad. Nauk SSSR 226, 1299–1302.Google Scholar
Gubaidullin, A. A., Ivandaev, A. I., Nigmatulin, R. I. & Khabeev, N. S. 1982 Waves in bubbly liquids. Advances in Science and Technology of VINITI (Itogi nauki i tekhniki VINITI). Ser. Mechanics of fluids and gases, vol. 17, pp. 160–249. Moscow.
Kalra, S. P. & Zvirin, Y. 1981 Shock wave-induced bubble motion. Intl. J. Multiphase Flow 7, 115–127.Google Scholar
Kogarko, B. S. 1961 On a cavitating liquid model, Dokl. Akad. Nauk SSSR, 137, 1331–1333.Google Scholar
Kutateladze, S. S., Burdukov, A. P., Kuznetsov, V. V., Nakoryakov, V. E., Pokusaev, B. G. & Shreiber, I. R. 1972 Structure of weak shock waves in a gas–liquid medium. Dokl. Akad. Nauk SSSR, 207, 313–315.Google Scholar
Kuznetsov, V. V., Nakoryakov, V. E., Pokusaev, B. G. & Shreiber, I. R. 1978 Propagation of perturbations in a gas–liquid mixture. J. Fluid Mech. 85, 85–96.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1976 Statistical Physics. Moscow: Nauka.
Nagiev, F. B. & Khabeev, N. S. 1981 Growth and collapse of vapour bubbles in boiling liquid. Zh. Prikl. Mekh. Tekh. Fiz. 5, 100–106.Google Scholar
Nakoryakov, V. E., Pokusaev, B. G., Pribaturin, N. A. & Shreiber, I. R. 1984 Shock waves in boiling liquids. Intl Commum. Heat Mass Transfer 11, 55–62.Google Scholar
Nakoryakov, V. E. & Shreiber, I. R. 1979 Model of propagation of perturbations in a vapour–liquid mixture. Teplo fiz. Vys. Temp. 4, 798–803.Google Scholar
Nigmatulin, R. I. 1978 Fundamentals of the Mechanics of Heterogenous Media. Moscow: Nauka.
Nigmatulin, R. I. 1979 Spatial averaging in the mechanics of heterogeneous and dispersed systems. Intl. J. Multiphase Flow 5, 353–385.Google Scholar
Nigmatulin, R. I. 1982 Mathematical modelling of bubbly liquid motion and hydrodynamical effects in wave propagation phenomena. Appl. Sci. Res. 38, 267–289.Google Scholar
Nigmatulin, R. I. & Khabeev, N. S. 1974 Heat transfer between a gas bubble and a liquid. Izv. Akad. Nauk SSSR, Mekh. Zhid. i Gaza 5, 94–100.Google Scholar
Nigmatulin, R. I. & Khabeev, N. S. 1975 Dynamics of vapour bubbles. Izv. Akad. Nauk SSSR, Mekh. Zhid. i Gaza 3, 59–67.Google Scholar
Nigmatulin, R. I., Khabeev, N. S. & Nagiev, F. B. 1979 Fragmentation and collapse of vapour bubbles and enhancement of shock waves in a liquid with vapour bubbles. In Gas and Wave Dynamics, 3, (ed. Kh. A. Rakhmatulin), pp. 124–129. Moscow State University.
Nigmatulin, R. I., Khabeev, N. S. & Nagiev, F. B. 1981 Dynamics, heat and mass transfer of vapour-gas bubbles in liquid. Intl. J. Heat and Mass Transfer 24, 1033–1044.Google Scholar
Nigmatulin, R. I., Khabeev, N. S. & Shagapov, V. Sh. 1974 Shock waves in a liquid with gas bubbles. Dokl. Akad. Nauk SSSR 214, 779–782.Google Scholar
Nigmatulin, R. I. & Shagapov, V. Sh. 1974 Structure of shock waves in a liquid containing gas bubbles. Izv. Akad. Nauk SSSR, Mekh. Zhid. i Gaza 6, 30–41.Google Scholar
Nigmatulin, R. I., Shagapov, V. Sh., Vakhitova, N. K. & Shikhmurzaeva, Z. A. 1982 Shock waves in a liquid with vapour bubbles. Inzh. Phys. Zh. 27, 192–206.Google Scholar
Noordzij, L. 1973 Shock waves in bubbly liquid mixtures. In Proc. IUTAM Symp. on Nonsteady Flow of Water at High Speeds (ed. L. I. Sedov & G. Yu. Stepanov), pp. 369–374. Moscow: Nauka.
Noordzij, L. & Van Wijngaarden, L. 1974 Relaxation effects, caused by relative motion, on shock waves in gas-bubble liquid mixtures. J. Fluid Mech. 66, 115–143.Google Scholar
Parkin, B. R., Gilmore, F. R. & Brode, H. L. 1961 Shock waves in bubbly water. Memorandum RM-2795-PR, (Abridged).
Plesset, M. S. & Prosperetti, A. 1977 Bubble dynamics and cavitation. Ann. Rev. Fluid Mech. 9, 145–185.Google Scholar
Pokusaev, B. G. 1979 Pressure waves in bubbly gas and vapour–liquid media. In: Hydrodynamics and Heat Transfer in One- and Two-Phase Media (ed. V. E. Nakoryakov), pp. 26–36. Institute of Thermal Physics SD Academy of Sciences of the USSR, Novosibirsk.
Sedov, L. I. 1984 Mechanics of Continua. Moscow: Nauka.
Tan, M. J. & Bankoff, S. G. 1984 Propagation of pressure waves in bubbly mixtures. Phys. Fluids 27, 1362–1369.Google Scholar
Trammell, G. T. 1962 Sound waves in water containing vapour bubbles. J. Appl. Phys. 33, 1662–1670.Google Scholar
Van Wijngaarden, L. 1970 On the structure of shock waves in liquid–bubble mixtures. Appl. Sci. Res. 22, 366–381.Google Scholar
Van Wijngaarden, L. 1972 One-dimensional flow of liquids containing small gas bubbles. Ann. Rev. Fluid Mech. 4, 369–396.Google Scholar
Ngok Hai Zuong & Khabeev, N. S. 1983 On some approach to the heat problem for the vapour–liquid medium of bubbly structure. Teplofiz. Vys. Temp. 1, 137–145.Google Scholar
Ngok Hai Zuong, Nigmatulin, R. I. & Khabeev, N. S. 1982 Structure of shock waves in a liquid with vapour bubbles. Izv. Akad. Nauk SSSR, Mekh. Zhid. i Gaza 2, 109–118.Google Scholar
Ngok Hai Zuong, Nigmatulin, R. I. & Khabeev, N. S. 1984 Unsteady waves in a liquid with vapour bubbles. Izv. Akad. Nauk SSSR, Mekh. Zhid. i Gaza 5, 117–125.Google Scholar