Nonlinear Effects in Bubbly Liquid with Shock Waves
The paper presents the results of theoretical and
numerical modeling of propagation of shock waves in bubbly liquids
related to nonlinear effects (realistic equation of state, chemical
reactions, two-dimensional effects). On the basis on the Rankine-
Hugoniot equations the problem of determination of parameters of
passing and reflected shock waves in gas-liquid medium for
isothermal, adiabatic and shock compression of the gas component is
solved by using the wide-range equation of state of water in the
analitic form. The phenomenon of shock wave intensification is
investigated in the channel of variable cross section for the
propagation of a shock wave in the liquid filled with bubbles
containing chemically active gases. The results of modeling of the
wave impulse impact on the solid wall covered with bubble layer are
presented.
[1] R. I. Nigmatulin, Dynamics of Multiphase Media. Moscow: Nauka, vol.
1-2, 1987.
[2] A. I. Sychev, "Strong shock waves in bubble media," Zh. Tekh. Fiz., vol.
80, no. 6, pp. 31-35, 2010.
[3] B. E. Gelfand, S. A. Gubin, and E. I Timofeev, "Reflection of plane
shock waves from a solid wall in a gas bubble-liquid system," Fluid
Dynamics, vol.13, no. 2, pp. 306-310, 1978.
[4] U. O. Agisheva, R. Kh. Bolotnova, V. A. Buzina, M. N. Galimzianov
"Parametric analysis of the regimes of shock-wave effects on the gasliquid
media," Fluid Dynamics, 2012, submitted for publication.
[5] R. I. Nigmatulin, R. Kh. Bolotnova, "Wide range equation of state for
water and steam. Reductive form of molecular phase," High
Temperature, vol. 49, no. 2, pp. 310-313, 2011.
[6] I. J. Campbell, A. S. Pitcher, "Shock waves in a liquids containing gas
bubbles," in Proc. of the Royal Society of London, A.243, no. 1235, pp.
534-545, 1958.
[7] Kh. A. Rakhmatulin, "Wave propagation in multicomponent media,"
Prikladnaya Matematika i Mekhanika, vol. 33, no. 4, pp. 598-601, 1969.
[8] Y. B. Zeldovich, Yu. P. Raizer, Physics of Shock Waves and High-
Temperature Hydrodynamic Phenomena. Prinston: Academic Press,
1966.
[9] V. S. Surov, "Shock adiabat of a one-velocity heterogeneous medium,"
J. of Engineering Physics and Thermophysics, vol. 79, no. 5, pp.886-
892, 2006.
[10] R. Kh. Bolotnova, ð£. N. Galimzianov, and U. ð×. Agisheva, "Modeling
of the strong shock waves interaction in gas-liquid mixtures," Izv.
Vysshikh Uchebnykh Zavedeniy. Povolzhskii Region . Fiz.-Math. Nauki,
no. 2, pp. 3-14, 2011.
[11] R. I. Nigmatulin, V. Sh. Shagapov, I. K. Gimaltdinov, and F. F.
Akhmadulin, "Explosion of a bubble curtain with a combustible-gas
mixture under the action of a pressure pulse" // Doklady Physics, Vol.
48, pp. 75-79, 2003.
[12] R. I. Nigmatulin, R. Kh. Bolotnova, N. K. Vakhitova, A. S. Topolnikov,
S. I. Konovalova, and N. A.Makhota, "Amplification of compression
waves in clean and bubbly liquids", Proc. of World Academy of Science,
Engineering and Technology, vol. 58, pp.188-193, 2009.
[13] A. I. Sychev, "Influence of bubble size on the characteristics of
detonation wave", Phyz. Gor. Vzr., vol. 31, No. 5, pp.83-91, 1995.
[14] R. I. Nigmatulin, V. Sh. Shagapov, I. K. Gimaltdinov, and M. N.
Galimzyanov, "Two-dimensional pressure waves in liquid with bubbly
zone", Doklady Physics, vol. 46, no 6, pp. 445-451, 2001.
[15] R. I. Nigmatulin, V. Sh. Shagapov, and N. K. Vakhitova, "Expression of
bearing phase compressibility in bubbly media under shock waves,"
Soviet Physics Doklady, vol. 304, no. 5, pp. 1077-1088, 1989.
[16] A. A. Samarskiy, Yu. P. Popov, Difference Methods for Solving Gas
Dynamics Problems. Moscow: Nauka, 1980.
[1] R. I. Nigmatulin, Dynamics of Multiphase Media. Moscow: Nauka, vol.
1-2, 1987.
[2] A. I. Sychev, "Strong shock waves in bubble media," Zh. Tekh. Fiz., vol.
80, no. 6, pp. 31-35, 2010.
[3] B. E. Gelfand, S. A. Gubin, and E. I Timofeev, "Reflection of plane
shock waves from a solid wall in a gas bubble-liquid system," Fluid
Dynamics, vol.13, no. 2, pp. 306-310, 1978.
[4] U. O. Agisheva, R. Kh. Bolotnova, V. A. Buzina, M. N. Galimzianov
"Parametric analysis of the regimes of shock-wave effects on the gasliquid
media," Fluid Dynamics, 2012, submitted for publication.
[5] R. I. Nigmatulin, R. Kh. Bolotnova, "Wide range equation of state for
water and steam. Reductive form of molecular phase," High
Temperature, vol. 49, no. 2, pp. 310-313, 2011.
[6] I. J. Campbell, A. S. Pitcher, "Shock waves in a liquids containing gas
bubbles," in Proc. of the Royal Society of London, A.243, no. 1235, pp.
534-545, 1958.
[7] Kh. A. Rakhmatulin, "Wave propagation in multicomponent media,"
Prikladnaya Matematika i Mekhanika, vol. 33, no. 4, pp. 598-601, 1969.
[8] Y. B. Zeldovich, Yu. P. Raizer, Physics of Shock Waves and High-
Temperature Hydrodynamic Phenomena. Prinston: Academic Press,
1966.
[9] V. S. Surov, "Shock adiabat of a one-velocity heterogeneous medium,"
J. of Engineering Physics and Thermophysics, vol. 79, no. 5, pp.886-
892, 2006.
[10] R. Kh. Bolotnova, ð£. N. Galimzianov, and U. ð×. Agisheva, "Modeling
of the strong shock waves interaction in gas-liquid mixtures," Izv.
Vysshikh Uchebnykh Zavedeniy. Povolzhskii Region . Fiz.-Math. Nauki,
no. 2, pp. 3-14, 2011.
[11] R. I. Nigmatulin, V. Sh. Shagapov, I. K. Gimaltdinov, and F. F.
Akhmadulin, "Explosion of a bubble curtain with a combustible-gas
mixture under the action of a pressure pulse" // Doklady Physics, Vol.
48, pp. 75-79, 2003.
[12] R. I. Nigmatulin, R. Kh. Bolotnova, N. K. Vakhitova, A. S. Topolnikov,
S. I. Konovalova, and N. A.Makhota, "Amplification of compression
waves in clean and bubbly liquids", Proc. of World Academy of Science,
Engineering and Technology, vol. 58, pp.188-193, 2009.
[13] A. I. Sychev, "Influence of bubble size on the characteristics of
detonation wave", Phyz. Gor. Vzr., vol. 31, No. 5, pp.83-91, 1995.
[14] R. I. Nigmatulin, V. Sh. Shagapov, I. K. Gimaltdinov, and M. N.
Galimzyanov, "Two-dimensional pressure waves in liquid with bubbly
zone", Doklady Physics, vol. 46, no 6, pp. 445-451, 2001.
[15] R. I. Nigmatulin, V. Sh. Shagapov, and N. K. Vakhitova, "Expression of
bearing phase compressibility in bubbly media under shock waves,"
Soviet Physics Doklady, vol. 304, no. 5, pp. 1077-1088, 1989.
[16] A. A. Samarskiy, Yu. P. Popov, Difference Methods for Solving Gas
Dynamics Problems. Moscow: Nauka, 1980.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:63195", author = "Raisa Kh. Bolotnova and Marat N. Galimzianov and Andrey S. Topolnikov and Uliana O. Agisheva and Valeria A. Buzina", title = "Nonlinear Effects in Bubbly Liquid with Shock Waves", abstract = "The paper presents the results of theoretical and
numerical modeling of propagation of shock waves in bubbly liquids
related to nonlinear effects (realistic equation of state, chemical
reactions, two-dimensional effects). On the basis on the Rankine-
Hugoniot equations the problem of determination of parameters of
passing and reflected shock waves in gas-liquid medium for
isothermal, adiabatic and shock compression of the gas component is
solved by using the wide-range equation of state of water in the
analitic form. The phenomenon of shock wave intensification is
investigated in the channel of variable cross section for the
propagation of a shock wave in the liquid filled with bubbles
containing chemically active gases. The results of modeling of the
wave impulse impact on the solid wall covered with bubble layer are
presented.", keywords = "bubbly liquid, cavitation, equation of state, shock
wave", volume = "6", number = "8", pages = "1200-8", }