1-1(81) 2014 PHYSICAL SCIENCE
D.I. Popov , R.M. Utemesov
Low-Dimensional Approximation of Rayleigh-Benard Convection Problem for Two-Phase Mixture
The Rayleigh-Benard convection problem in a horizontal layer of a two-phase mixture heated from below is considered. The model of disperse flow is described with the Eulerian approach of interpenetrating motion of two continua. Two-fluid velocity and temperature field equations are used to describe heat and mass transfer in mixture. The carrier medium is concerned as incompressible viscous gas and dispersed phase is concerned as gas without tangential and normal tensiones. The low-order dynamical system, generalized Lorenz equations for two-phase flow, is obtained. It is shown that in the case of disperse flow the stability conditions of the stationary solution are modified and the description of that conditions includes the parameter characterizing interfacial viscous force. The critical Rayleigh number increases. Phase portraits of dynamical system at various Rayleigh numbers are numerically obtained. With numerical results, we can see transformation of transition to chaotic motion for disperse flow. For example, one can observe the attractor, type of Lorentz attractor, at values of Rayleigh number corresponding to strongly chaotic homogeneous flow.
DOI 10.14258/izvasu(2014)1.1-51
Key words: Rayleigh-Benard problem , two-phase flow , nonlinear dynamics
Full text at PDF, 402Kb. Language: Russian.
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