Title: 3D computer simulation of Rayleigh-Benard instability in a square box

Authors: E.E. Fedoseev, V.V. Kolmychkov, O.S. Mazhorova

Addresses: Keldysh Institute of Applied Mathematics RAS, Moscow 125047, Russia. ' Keldysh Institute of Applied Mathematics RAS, Moscow 125047, Russia. ' Keldysh Institute of Applied Mathematics RAS, Moscow 125047, Russia

Abstract: The paper presents the numerical study for Rayleigh-Benard convection in a square box with rigid boundaries. The process is described by 3D time-dependent Navier-Stokes and heat transfer equations. The liquid is supposed to be incompressible and Boussinesq approximation is adopted. At initial moment temperature field is disturbed with two dimensional disturbance in the form 0.02 cos(k₀x), where k₀ is initial wave number. The flow pattern evolution is analysed for different Rayleigh number (Ra) values with respect to k₀. Computer simulation has been done for 1.7 × 10³ < Ra < 1.1 × 10⁴, Pr = 0.71; 1, 0.5 < k₀ < 5.5. Skewed varicose, oscillatory, spiral defect chaos instabilities have been registered. Also convection of the fluids with the temperature dependent physical properties and internal heating, convective instability of electrically conducting fluid in the presence of a static magnetic field are studied. It provides an additional possibility to control convective flow in Rayleigh-Bernard problem.

Keywords: convective instability; computer simulation; Rayleigh-Bernard convection; roll pattern; skewed varicose instability; oscillatory convection; spiral defect chaos; stability; electrically conducting fluids; uniform external magnetic field; internal heating; variable material properties; convective flow.

DOI: 10.1504/PCFD.2010.034450

Progress in Computational Fluid Dynamics, An International Journal, 2010 Vol.10 No.4, pp.208 - 217

Published online: 04 Aug 2010 *

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