Thermal convection inside an oscillating cube analysed with proper orthogonal decomposition

Abstract

We reveal the fundamental and dominant flow structures of thermal convection in a cubic cavity under forced oscillation heated differentially by analysing the flow field with the proper orthogonal decomposition (referred to as POD). The database is made of consequtive series of three-dimensional results obtained by the direct numerical simulation based on the Boussinesq approximation for a forcedly-oscillating cube under the zero-gravity environment, at vibrational Rayleigh number (the Rayleigh number based on the cavity's acceleration amplitude instead of the gravitational acceleration) Raη = 5.0×104 - 1.1×105, Plandtl number Pr = 7.1 (water) and non-dimensional forced-oscillating frequency ω = 1.0×100 - 2.0×102. The direction of the forced sinusoidal oscillation is parallel to the temperature gradient. It appears that the most energetic POD modes, or the first POD eigenfunctions with large eigenvalues, account for the transient process on flow structures during one forcing cycle. The first eigenfunctions correspond to the steady and laminar flow structures which appear inside a non-oscillating cube in the terrestrial environments. The POD expansion coefficient is found to be useful for predicting a consecutive series of the dominant flow structures.

Keywords

• rayleigh-bénard convection
• forced vibration
• pod
• pca
• kl expansion
• laminar flow
• unsteady flow