### Abstract

This work outlines a mathematical model of the pressure wave propagation in the gas media containing different liquid particles such as water droplets and offers the method to estimate the influence of the energy exchange between phases on the evolution of the wave under different conditions of the interphase interactions. Conservation equations describing the propagation and structure of finite amplitude perturbations in such a medium, with correction for heat transfer and momentum exchange between the phases have been employed to obtain an evolution of the wave profile during of the pressure wave propagation. Such a media is dispersive due to the finite rate of the above exchange processes. The resultant equations in general incorporate integral terms containing the amplitude of the perturbation. The derived equations are capable of describing the evolution of waves at any ratio between time of the internal process and the characteristic period of the pressure wave. The solutions can be used for determining the dissipation of energy of a wave passing through a medium containing liquid droplets. The proposed approach neglects the effect of droplets' temperature influence on the gas bulk. Two extreme cases have been considered, one for long-wave and the other one for short-wave interaction. Final results show that there are analytical solutions for some of the specific cases of the interaction between phases. The finding could be used for estimation of wave dissipation in medium containing different liquid particles.

Original language | English |
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Title of host publication | 18th Australasian Coastal and Ocean Engineering Conference 2007 and the 11th Australasian Port and Harbour Conference 2007, COASTS and PORTS 2007 |

Pages | 791-796 |

Number of pages | 6 |

Publication status | Published - 2007 |

Externally published | Yes |

Event | 18th Australasian Coastal and Ocean Engineering Conference 2007, COASTS 2007 and the 11th Australasian Port and Harbour Conference 2007, PORTS 2007 - Melbourne, VIC, Australia Duration: Jul 18 2007 → Jul 20 2007 |

### Other

Other | 18th Australasian Coastal and Ocean Engineering Conference 2007, COASTS 2007 and the 11th Australasian Port and Harbour Conference 2007, PORTS 2007 |
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Country | Australia |

City | Melbourne, VIC |

Period | 7/18/07 → 7/20/07 |

### Fingerprint

### ASJC Scopus subject areas

- Ocean Engineering

### Cite this

*18th Australasian Coastal and Ocean Engineering Conference 2007 and the 11th Australasian Port and Harbour Conference 2007, COASTS and PORTS 2007*(pp. 791-796)

**Mathematical model of interaction between finite amplitude wave and the liquid particles.** / Vakhguelt, Anatoli.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*18th Australasian Coastal and Ocean Engineering Conference 2007 and the 11th Australasian Port and Harbour Conference 2007, COASTS and PORTS 2007.*pp. 791-796, 18th Australasian Coastal and Ocean Engineering Conference 2007, COASTS 2007 and the 11th Australasian Port and Harbour Conference 2007, PORTS 2007, Melbourne, VIC, Australia, 7/18/07.

}

TY - GEN

T1 - Mathematical model of interaction between finite amplitude wave and the liquid particles

AU - Vakhguelt, Anatoli

PY - 2007

Y1 - 2007

N2 - This work outlines a mathematical model of the pressure wave propagation in the gas media containing different liquid particles such as water droplets and offers the method to estimate the influence of the energy exchange between phases on the evolution of the wave under different conditions of the interphase interactions. Conservation equations describing the propagation and structure of finite amplitude perturbations in such a medium, with correction for heat transfer and momentum exchange between the phases have been employed to obtain an evolution of the wave profile during of the pressure wave propagation. Such a media is dispersive due to the finite rate of the above exchange processes. The resultant equations in general incorporate integral terms containing the amplitude of the perturbation. The derived equations are capable of describing the evolution of waves at any ratio between time of the internal process and the characteristic period of the pressure wave. The solutions can be used for determining the dissipation of energy of a wave passing through a medium containing liquid droplets. The proposed approach neglects the effect of droplets' temperature influence on the gas bulk. Two extreme cases have been considered, one for long-wave and the other one for short-wave interaction. Final results show that there are analytical solutions for some of the specific cases of the interaction between phases. The finding could be used for estimation of wave dissipation in medium containing different liquid particles.

AB - This work outlines a mathematical model of the pressure wave propagation in the gas media containing different liquid particles such as water droplets and offers the method to estimate the influence of the energy exchange between phases on the evolution of the wave under different conditions of the interphase interactions. Conservation equations describing the propagation and structure of finite amplitude perturbations in such a medium, with correction for heat transfer and momentum exchange between the phases have been employed to obtain an evolution of the wave profile during of the pressure wave propagation. Such a media is dispersive due to the finite rate of the above exchange processes. The resultant equations in general incorporate integral terms containing the amplitude of the perturbation. The derived equations are capable of describing the evolution of waves at any ratio between time of the internal process and the characteristic period of the pressure wave. The solutions can be used for determining the dissipation of energy of a wave passing through a medium containing liquid droplets. The proposed approach neglects the effect of droplets' temperature influence on the gas bulk. Two extreme cases have been considered, one for long-wave and the other one for short-wave interaction. Final results show that there are analytical solutions for some of the specific cases of the interaction between phases. The finding could be used for estimation of wave dissipation in medium containing different liquid particles.

UR - http://www.scopus.com/inward/record.url?scp=84874158469&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84874158469&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781622764280

SP - 791

EP - 796

BT - 18th Australasian Coastal and Ocean Engineering Conference 2007 and the 11th Australasian Port and Harbour Conference 2007, COASTS and PORTS 2007

ER -