Abstract
An evolutionary equation with two nonlinearities (basic hydrodynamic and an additional nonlinearity attributable to interphase heat transfer) describing the wave dynamics in a mixture in the presence of viscosity is obtained. For a quasi-adiabatic regime, depending on the heat transfer laws determined by the relations between the thermophysical parameters of the mixture two exact particular solutions predicting different pressure behaviors in the wave are given. Nonmonotonous pressure behavior associated with an increase in the wave amplitude is interpreted as wave amplification as compared with the case of monotonous behavior. Depending on the thermophysical parameters, an interval of permissible Weber numbers is found for which the amplification effect is observed. The surface tension reduces the wave amplitude and width and results in a nonmonotonous dependence of the wave velocity on the Weber number.
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REFERENCES
B. E. Gel'fand, V. V. Stepanov, E. I. Timofeev, and S. A. Tsyganov, "Shock wave amplification in a nonequilibrium liquid-soluble gas bubble system," Dokl. Akad. Nauk SSSR, 239, No. 1, 71–73 (1978).
A. A. Borisov, B. E. Gel'fand, R. I. Nigmatulin, Kh. A. Rakhmatulin, and E. I. Timofeev, “Shock wave amplification in liquids with vapor and soluble gas bubbles,”Dokl. Akad. Nauk SSSR, 263, No. 3, 594–598 (1982).
V. E. Nakoryakov, B. G. Pokusaev, and I. R. Shreiber, Wave Dynamics of Gas-and Vapor-Liquid Media [in Russian], Energoatomizdat, Moscow (1990).
R. I. Nigmatulin, Dynamics of Multiphase Media. V.2, Hemisphere, Washington (1989).
V. G. Gasenko, V. E. Nakoryakov, and I. R. Shreiber, "Shock wave amplification in a liquid with gas bubbles," Dokl. Akad. Nauk SSSR, 253, No. 6, 1330–1332 (1980).
G. G. Oganyan, "Effect of interphase heat transfer on nonlinear wave propagation in a gas-liquid mixture," Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 5, 77–87 (2000).
J. Weiss, M. Tabor, G. Carnevale, "The Painlevé property for partial differential equation," J. Math. Phys., 24, No. 3, 522–526 (1983).
N. A. Kudryashov, "Exact soliton solutions of a generalized evolutionary equation of wave dynamics," Prikl. Matem. Mekh., 52, No. 3, 465–470 (1988).
N. A. Kudryashov and M. B. Sukharev, "Exact solutions of a nonlinear fifth-order equation describing waves on water," Prikl. Matem. Mekh., 65, No. 5, 884–894 (2001).
G. G. Oganyan, "On the nonlinear wave structures in a thermally relaxing gas-liquid mixture," Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 2, 110–119 (2002).
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Oganyan, G.G. Effects of Interphase Heat Transfer and Surface Tension on Nonlinear Wave Propagation in a Gas-Liquid Mixture. Fluid Dynamics 38, 724–733 (2003). https://doi.org/10.1023/B:FLUI.0000007834.21806.94
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DOI: https://doi.org/10.1023/B:FLUI.0000007834.21806.94