International Conference «Mathematical and Information Technologies, MIT-2016»

28 August – 5 September 2016

Vrnjacka Banja, Serbia – Budva, Montenegro

Perepechko Y.   Sorokin K.  

Two-phase convection in acoustic field

Reporter: Perepechko Y.

Convective heat and mass transfer plays an important role in the evolution of geological fluid systems and determines hydrodynamic processes in the lithosphere, associated with igneous volcanism, mineralization, etc. The interest to the study of heat and mass transfer in fluid / fluid-magmatic systems in the presence of internal acoustic sources is caused by the seismic activity in the lithosphere. In applied works concerned with the study of convection in liquids under acoustic or vibratory exposure, usually anacoustic approximation of incompressibility of the medium is employed. The study of thermoacoustic convection has been conducted for single-phase liquids [1, 2]. The influence of acoustic effects on convection in complex media is poorly studied. In this paper we investigate the influence of the compressibility of heterophase media on convective flows under the influence of acoustic vibrations of different frequencies as well the stability of convective flows. We consider the dynamics of two-velocity compressible media such as a saturated granular medium. The equations of thermodynamically consistent two- velocity model of compressible two-phase medium [3] are obtained through the conservation laws method [4, 5]. Computational implementation of the model is based on the control volume method [6], which ensures the integral conservation of basic quantities at digitalization of differential equations. For an adequate description of acoustic processes, the correct consideration of the compressibility of the medium was carried out in the framework of the proposed model and numerical simulation. The SIMPLE iterative procedure was modified to account for nonequilibrium nature of the medium in terms of pressure in the phases [7]. The paper presents the results of numerical simulation of Rayleigh-Benard thermal convection in a flat layer of two-phase medium, heated from below. The perturbations behavior near the stability threshold of thermoacoustic flow of two-phase media was investigated to obtain the conditions for the transition from stationary regime of diffusion heat transfer to the convective heat and mass transfer initiated by high frequency acoustic impact, which was generated by the internal final small source.
This work was supported by Russian Foundation for Basic Research, grant #16-01-00729a, and the Ministry of Education and Science of the Russian Federation, agreement #14.607.21.0106 (the unique identifier of the project RFMEFI60714X0106).

[1] D. V. Lyubimov, and S. V. Shklyaev, "Thermal Convection in an Acoustic Field," Fluid Dynamics 35, 321, 2000.
[2] B. Lia, X. Hana, Z. Wana, X. Wangb, Y. Tang, "Influence of Ultrasound on Heat Transfer of Copper Tubes with Different Surface Characteristics in Sub-cooled Boiling," Applied Thermal Engineering 92, 93, (2016).
[3] Yu. V. Perepechko, and K. E. Sorokin, "Two-velocity Dynamics of Heterophase Media," Journal of Engineering Thermophysics 22, 241.
[4] L. D. Landau, "The Theory of Superfluidity of Helium II," Journal of Physics, USSR, 5, (1941).
[5] V. N. Dorovsky, "Mathematical Models of Two-velocity Media, Mathematical and Computer Modelling 21, 17, (1995).
[6] S. V. Patankar, D. B. Spalding, "A Calculation Procedure for Heat, Mass and Momentum Transfer in Three-dimensional Parabolic Flows," International Journal of Heat and Mass Transfer 15, 1787, (1972).
[7] K. C. Karika, S. V. Patankar, "Pressure Based Calculation Procedure for Viscous Flows at All Speeds in Arbitrary Configurations," AIAA Journal 27, 1167, (1989).

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